Peter Houston has hinted that he may leave his post as Dundee United manager at the end of the season as he has yet to be approached about a new contract.

The coach has enjoyed relative success since taking over at Tannadice, winning the Scottish Cup in 2010 and taking the club into Europe.

He will be out of contract at the end of the season, though, and Houston has confirmed that his club have yet to come forward with a new deal. The 54-year-old, who doubles as assistant to Scotland manager Craig Levein, was linked to the vacant manager's post at Hearts this summer and his future is now up for debate once again.

United are enduring a modest start to the campaign but edged their way into the quarter-finals of the Scottish Communities League Cup on Wednesday night following a narrow win over Queen of the South. It was not a result which will likely feature highly in his list of Tannadice memories, but Houston believes he has plenty of positives to look back on if his tenure is to come to an end after this season.

"There is nothing on the table for me. A lot of people have been asking me why I haven't signed a new deal; because I have not been offered one basically," said the United manager. "Who knows what will happen. The chairman has not gone back to John Colquhoun [Houston's agent].

"If it's to be the end of May when I move on from here then I'll look back with fond memories. But, in saying that, there might be an offer put on the table for me. I don't know.

"It's a wee bit early to jump into things just now. John Colqhoun is waiting on a phone call from the chairman, no doubt the chairman has a lot of issues to deal with. I'd expect the chairman to get in touch because that's what John is waiting on, a phone call from him."

His immediate focus will revert to more pressing club matters today, with United in the Highlands to take on Inverness Caledonian Thistle tomorrow. Inverness have also had a relatively slow start to the season – they have yet to win in the league and needed penalties to overcome Stenhousemuir in the League Cup – but Houston is not inclined to take them lightly.

"I've watched Inverness a couple of times this season live and maintain they're a decent side," said the United manager. "You never get it easy against Inverness and I'm not expecting that to be any different this time.

"Even the Old Firm have vouched in the past for how hard it is to actually go up there and win. If you go to the Caledonian Stadium and come away with the three points then you've won a watch.

"We had to come from 2-0 down there to win 3-2 last season when we had to show a lot of character. Again Terry [Butcher, the Inverness manager] has had to rebuild his side after losing so many players he's done a fantastic job. Richie Foran is a quality player and Andrew Shinnie just behind him is high in quality so we'll have to be really on our toes."

Houston hopes his players are able to build on their League Cup victory over Queens and praised them for weathering a tempestuous second half as the second division leaders rallied. "You can't win playing against the lower league clubs like Queen of the South," he said.

"I think a lot of people thought there might have been a cup shock at Palmerston because of our recent league form. We had to hang on in the end but having seen them I'm sure Queen of the South will end up winning the second division.

"The important thing is we got the reaction we were looking for after the Hearts defeat a few days earlier and kept another clean sheet."