But the 31-year-old insisted he will be in position to decide whether he takes part at Wimbledon, which starts on Monday, by the time the draw is made on Friday.
"Yeah, probably. I'll chat with my team in the next couple of days," said Murray.
"Obviously see how I pull up again on Thursday, but I don't really anticipate any issues. With each match I'm trying to gain information about where I'm at physically and where my game is at,” he added.
Murray, a two-time Wimbledon champion, has slipped to 156 in the world after only returning to action at Queen's last week following 11 months out with a hip injury.
Murray not sure about Wimbledon after comeback defeat
The 31-year-old lost first up at Queen's against Nick Kyrgios but was buoyed by beating fellow three-time major winner Stan Wawrinka in the opening round at Eastbourne on Monday.
Murray suffered his hip injury in the quarter-finals at Wimbledon last year and underwent surgery in January.
This year's Wimbledon gets underway at the All England Club on Monday.
"The matches have been helpful. The match against Nick (Kyrgios, last week) was a significantly longer match. (Against Edmund) was very different," added Murray.
He continued, "I was reacting a lot on the court rather than being the one that was dictating on my own serve. They are the sort of things that when you play against the best players, which obviously Kyle is one of them just now, over the course of the match, that tells a little bit.
Surpassing Federer not on Nadal’s mind
"There is no risk of me playing tennis just now. It's just whether I feel like I'm able to do myself justice. Two weeks ago I practised with Kyle and I didn't win a game.
"So I have made decent improvements (over) the last couple of weeks and obviously have been somewhat competitive in the matches that I have played. But I don't just want to go out there to just play. I want to be able to compete properly.
"If I don't feel like I can do that, then I won't play. If I do and physically I feel ready, mentally I'm in the right place, then I'll go for it, but there's no danger about me injuring my hip more than there would be at any other stage,” he added.
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