It is probably fair to say that, having grown up outside the system and seen its failings as he has developed into a champion, Andy Murray is not the biggest fan of the Lawn Tennis Association.

Roger Draper's announcement that he is to step down as chief executive in September was greeted with delight by those who felt he had failed in his pledge to produce top players and spread the game at grassroots, while commanding an eye-watering salary.

But Murray knows how difficult it is to breed winners and get people to play the sport and believes the nub of the problem is the constant back-stabbing and in-fighting inside the LTA. If things are to improve, Murray says, that has to stop.

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"There are a lot of great people in British tennis," Murray explained as he prepared to face Juan Martin Del Potro today in the quarter-finals of the BNP Paribas Open. "None of them sees eye to eye and none of them speaks to each other. I think if everyone got in a room and actually was mature about it and gave their opinions and put them across, I think they could come up with pretty good solutions."

"I think it's important to make sure that you get all of those people – guys who have been at the top of the game, coaches who have produced players, try to get them involved, try to get that passion back," he said.

"And from their side – because I've seen it and I've read about it – just stop the negativity and, like, do something constructive with your ideas instead of just panning the LTA. It doesn't really work."

As thoughts turned to who might succeed Draper, who was paid £640,000, including a bonus of £200,000, the name of Judy Murray was suggested in some quarters. A smile came across Murray's lips. "She won't be doing that job," he said.

Murray said he expected the new chief to be British just because they need to genuinely care about tennis in the country to succeed. But though he ruled out Judy, he admitted she might be a good person to discuss how things can be improved.

"Her No.1 strength is working with kids," he said. "She doesn't have a place just to work out of in Scotland and we've obviously developed decent players; we've got three players playing here – my brother [Jamie], Colin [Fleming] and myself were all from one tiny little area in Scotland.

"She knows what it takes to set up a programme that's going to work for young kids so I think that's where her input would be most valuable. She speaks with the LTA a lot, she still does bits and pieces for them and obviously with the Fed Cup and stuff, she's still involved. It's a pretty big role she has anyway."

Murray said he would be happy to talk to the LTA if it felt he could be useful, especially in terms of how to train and produce players, but said he does not know too much about how to improve participation at grassroots.

The world No.3 said there were probably too many people working at the LTA but said the key was that everyone involved should be open enough to work together for the greater good.

"There needs to be a willingness from the personnel, really, to want to do it," he said. "If they do, then that's great because we have good coaches, we have players who were solid pros who weren't necessarily unbelievably talented but guys who have made the most of their games, and I think they can all help.

"I don't know the perfect solution, I don't think anyone does, but it will be interesting to see which route they go down because it's obviously a big decision."

Murray leads Del Potro 5-1 in their head-to-heads but surprisingly they have not played since 2009.

"I've played well against him in the past," Murray said. "I think my game against the bigger guys has worked well; using a lot of variety and being able to put the ball in awkward positions for them. But if I don't play well or use that style well on the day, then I'm not going to win."