Murray has struggled for fitness over the last two years and required hip resurfacing surgery in January so save his tennis career.
The three-time Grand Slam winner has had only positive signs since returning to the ATP tour, albeit he is competing in the less-durable doubles events.
After winning the Queen’s Club title alongside Feliciano Lopez, Murray crashed out of Eastbourne and Wimbledon in the early stages.
However, there was positives in the mixed doubles draw of his one Grand Slam playing alongside Serena Williams.
And Murray can now start to ramp up his comeback as he aims to play singles at the Cincinnati Masters in two weeks.
But there is one part of his game worrying the Brit as he prepares to do all of the running for himself again.
“My cardio isn’t great,” Murray said.
“In terms of how I’m moving and feeling and pulling up the next day from these practices, I’m really happy with where I’m at.
“I think I’m quite close. If I was to play a tournament in a few weeks’ time, I could do it.
“But it’s just to get to maybe where I want to get to, I’ll need to play matches and get a little bit more work done in the gym on my cardio.”
Before any definitive singles decision is made, Murray will play alongside brother Jamie in the Washington Open doubles draw this week.
They take on French pair Nicolas Mahut and Edouard Roger-Vasselin tonight.
And Murray is hoping to time on court will help in the race back to full fitness.
“What I’m doing here is, for the most part, I’m going to practise singles and play doubles to compete and then just each week I’m just going to see,” Murray added.
“If I keep progressing and I feel good in three weeks’ time, then I’ll play singles as soon as I’m ready.
“I’m not quite ready at this week, but I hope at some stage soon I will be.”