Andy Murray was continuing to mull over whether to play singles at Wimbledon after a practice session on Monday afternoon.

The 37-year-old showed definite signs of improvement hitting against fellow British player Kyle Edmund but remains unsure whether he is in good enough physical shape to play his first-round match against Czech Tomas Machac on Tuesday.

Murray was leading Edmund 6-3 2-0 when they reached the end of their session, and he said afterwards: “It was good.

“I’m going to go and have a chat with my team now, speak to my family this evening and then make a decision. It’s getting better and the testing and stuff I’ve done has been good, I just need to decide whether it’s enough to compete.”

Murray, who underwent surgery to remove a spinal cyst nine days ago, was serving well and hitting some strong groundstokes but his movement undoubtedly remains compromised and he was struggling when pulled out wide.

Machac, ranked 39, is certainly no mug and is likely to make the match physical, although he is inexperienced on grass.

While Murray is understandably desperate to make a final singles appearance at the All England Club before retirement, he would want to be able to give a good account of himself.

Murray’s indecision provides a headache for Wimbledon organisers in terms of Tuesday’s order of play, but chief executive Sally Bolton said: “We’ve always got plenty of scheduling challenges to face.

“As he said himself, Andy has earned the right to make the decision and we will absolutely respect that.

READ MORE: Novak Djokovic confident he'll be fit to start his Wimbledon campaign

“All of us have therefore got to be agile in the way that we deliver our plans, but we’re really happy to do that. It’s very much for Andy to make this decision and make it at the right time for him.”

It would undoubtedly be a blow to the tournament if Murray is not able to compete, although there appears to be a very good chance that he will be fit enough to team up with his brother Jamie in doubles even if he decides against singles.

“We would love to see him on court,” said Bolton. “Of course, if he isn’t, we’ve got plenty of other tennis going on, but I know the fans will be absolutely desperate to see him play so we wish him well in getting on court.”

Bolton was keeping close to her chest Wimbledon’s plans for honouring Murray whenever his final moment at the All England Club comes.

“We have got a variety of plans sitting waiting to deliver,” she said. “It really is for Andy to make that call and we’ll be ready whenever that happens. There’s been various conversations ongoing for some time now. Andy of course is very focused on his performance, not really on anything else.

“Once he decides to retire and we all get the chance to celebrate him I think you’ll really see how much he has meant to not just the tennis-loving public but the sports-loving public in the UK. I think there’ll be tears around the house.”

Murray confirmed last week that he is planning for Wimbledon and the Olympics to be the final events of his career.

Bolton hinted that the 37-year-old will join Fred Perry in having a statue somewhere in the grounds once his playing career is over, but that may not be outside Centre Court.

“You could argue that’s a bit of an obvious location,” she said. “As we reflect on the shape of these grounds and we think about the potential development over the road, we’ve got time to think about where any kind of physical celebration of Andy’s career might be.

“And, in any event, we’d want to work with Andy on that and he understandably is not ready to have those conversations just yet. We will make sure we get this right because this is for all time.”