Andy Murray may leave the decision over his Wimbledon participation until the weekend before the tournament begins.
Murray is up to ninth place in the world rankings
Murray pulled out of the French Open and this week's Artois Championships at Queen's Club after damaging his wrist in the Hamburg Masters last month.
"Hopefully by next week I'll be playing points and will make a decision around the weekend," he told BBC Sport.
"I've been practising for the last 10 days. It's tough to say whether I'll be playing but it's getting much better."
The 20-year-old Scot and world number nine was speaking at a David Lloyd Leisure event.
He injured his wrist during his match against Filippo Volandri in the first round of the Hamburg Masters on 15 May.
Though Murray did not break any bones, his wrist was inflamed and he was forced to wear a cast.
He has only played two full matches since the Miami Masters Series event in March and faces a race against time to be fit for the start of Wimbledon on 25 June.
If I'm ready for Wimbledon then great but if not I'll get ready for the American hard court stretch
"It's been going well," said Murray. "Each day I've been playing a bit more, hitting the ball a bit harder.
"I'm not going into a match at Wimbledon without having played two or three sets of a practice match as hard as I can.
"I don't want to do anything to cause extra damage.
"If I'm ready for Wimbledon then great but if not I'll get ready for the American hard court stretch."
Meanwhile, five-time Wimbledon champion Bjorn Borg believes the nation's expectations should not be too high should Murray play.
"If he's fit and he feels like he can play, he should play, but the expectation should not be high because he has been injured," said the Swede.
"It's bad because he started the year very well, he's a great player, and he has the potential to win a Grand Slam, but not this year.
"In the future he will, but if he plays Wimbledon, people shouldn't have too high an expectation because, mentally, to win that sort of tournament is a tough task and you have to be ready to play five sets."
Borg, who won five Wimbledon titles in a row between 1976 and 1980, believes the young Scot has the potential to win a major title next year.
He added: "I like his game in general. He doesn't really have any weaknesses and he can play on all kinds of surfaces.
"He has the right attitude towards the game and the thing he has to work on are both the physical and mental side but he is still very young.
"I like his style. He's very unpredictable to his opponent and he can play fast or loose.
"He's in the top 10 in the world and he will definitely be a Grand Slam-winner in the future, maybe even next year if he stays clear of injuries."
Borg also ruled out the chances of former British number one Tim Henman, who was knocked out of Queen's on Tuesday by wild card Marin Cilic.
He said: "Tim has done a lot for British tennis. He's seen his best years, let's face it.
"I wish him the best of luck at Wimbledon but I don't think we should have too high expectations on Tim at Wimbledon."