Manchester United are unlikely to bid for another centre-back if they fail in their pursuit of Real Madrid's Sergio Ramos.

After claims Ramos wanted out of Real Madrid, United offered to swap David de Gea for the 29-year-old defender.

However, it has become increasingly apparent in recent weeks that proposal will not be accepted, with Real Madrid manager Rafael Benitez recently stating he was "100 per cent" sure Ramos would stay.

The former Sevilla defender has captained Madrid on their pre-season tour following the departure of long-standing skipper Iker Casillas, and reports in Spain claim Ramos is close to agreeing a new deal with the 10-time European champions.

Nicolas Otamendi has been viewed as a possible alternative for United should Ramos decide to stay at Real Madrid, but it is understood manager Louis van Gaal has no interest in the Valencia centre-back.

Van Gaal is thought to be happy to go into the new season without another centre-half if the Ramos move does not come off.

Sources at United point out that the club had the fourth best defensive record in the Barclays Premier League last year, although De Gea's excellent form was key to that record.

It is understood that Van Gaal is happy with his options at centre-back and there is a feeling that the defence will be better protected this year given that the United boss intends on using two holding midfielders as part of a 4-2-3-1 formation.

The United manager has been pleased with the performances of Phil Jones and Daley Blind on United's pre-season tour.

Van Gaal also has Chris Smalling, Marcos Rojo, Paddy McNair and Tyler Blackett as well as Jonny Evans, who may stay at the club despite speculation he will leave.

Van Gaal is also willing to use Michael Carrick at centre-back if needed and is more concerned about the lack of options he has in attack.

"We need still more speed in front and also more creativity," the Dutchman said.

"Bayern Munich have (Franck) Ribery and (Arjen) Robben, Chelsea – they have (Eden) Hazard and Willian – speed and creativity. Real Madrid – have (Cristiano) Ronaldo and (Gareth) Bale.

"Manchester United fans want us to compete with these teams. Barcelona have Neymar and (Lionel) Messi. (Ashley) Young has made a fantastic season. (Juan) Mata the same, with assists and goals but to win the Champions League we need speed also.

"That is why I think, maybe, we still have to buy a player with speed and creativity."

Carrick, meanwhile, has no qualms about fighting Bastian Schweinsteiger and Moran Schneiderlin for a place in the United first team this season.

After complaining about a lack of cover in midfield last season, Van Gaal spent more than £40million on Schweinsteiger, who arrived from Bayern Munich, and former Southampton man Schneiderlin this summer.

That means Carrick is no longer the automatic pick he was last season.

The player, who turned 34 on Tuesday, has no problem competing with the new arrivals though and hopes their introduction will be a positive move for the club as they look to compete on four fronts.

"You want the best players here, and it's good for the squad, for the team," Carrick said.

"Morgan is good player. He has done terrific. It's another step for him in his career and there's no better place to be.

"We all know what Basti brings. He is a terrific player and he'll have a big influence on us going forward."

Despite the fanfare surrounding his signing, Schweinsteiger has failed to impress so far on United's pre-season tour of the United States.

The German World Cup winner is yet to start a game, with Van Gaal preferring to use Carrick and Schneiderlin as holding midfielders in the 4-2-3-1 formation he has used in the three games so far.

Schweinsteiger looked relatively comfortable in the first game against Club America in Seattle, but Van Gaal described the midfielder's performance against San Jose Earthquakes as "bad" and he missed the 3-1 win over Barcelona with a minor injury.

The 30-year-old is fit to feature in United's final game of the tour against Paris St Germain in Chicago in the early hours of Thursday, however.

Another win would give United a 100 per cent record from their American tour.

Although he missed it through injury, Carrick is aware United won all their pre-season matches last season before accumulating just 13 points from their opening 10 Premier League matches.

"You can gauge what you can from these pre-season games, but Tottenham on the first day of the season is where you're judged the most, and we're well aware of that even after three good results," the United midfielder said.

That said, Carrick thinks United are in a much better position heading into the new season than they were 12 months ago.

"The manager has been here a longer time and we're now used to his way of playing," Carrick said.

"We've improved as a team by understanding his way. I think we're stronger in numbers, in strength and depth and in quality this year."

Goalkeeper Sergio Romero is available to face PSG, but may not do so having spent just two days with his new team-mates since signing a three-year deal with United.

Angel di Maria is still absent from the tour amid claims he is close to a move to the French champions.

There will be no chance to ask Van Gaal about Di Maria's situation on the eve of the game as United have decided not to hold a pre-match press conference in Illinois.