But the Blues boss also warned that the midfielder may have to be patient to regain his place.
Moxon missed out with a hip problem as United drew 2-2 with Northampton Town on Saturday.
Simpson instead deployed Jack Robinson in the centre alongside Dylan McGeouch and Alfie McCalmont.
The trio put in good showings but Moxon could be pushing to regain his place next weekend against one of United’s bottom-four rivals.
“I’m hoping he will be [back],” Simpson said of the Denton Holme favourite.
“If everything settles down properly with him we’re looking at him hopefully training by the middle of the week and hopefully he’ll be available for us.
“He didn’t have a chance in the end for [Saturday], he was still a bit sore from from where he had the injection in his hip.
“So we’ll wait and see how he goes.
Robinson wasn’t afraid to shoot on Saturday and hit the woodwork in the second half (Image: Ben Holmes)
“But I’ve got to say I thought the three boys in midfield were excellent [against Northampton]. So there’s every chance that they deserve another opportunity.”
Robinson, normally a left-sided defender, impressed with his adaptability in Saturday’s midfield role.
The former Middlesbrough man offered some left-sided balance in the centre of the park against the Cobblers.
And he performed well in other respects too, United’s manager felt.
“He gives a balance and a bit of bite as well, because he’s got a really good attitude,” said Simpson of Robinson.
“He’s got energy, he can tackle and he’s got a bloody good left foot. I like his ability, and he’s a good character to have around.
“I know he’s been frustrated [not to have played more].
“Jack Armer was one of the first I called in during the week to say I was putting him back in the team and what I expected.
“I’m sure at that point Robbo thought, ‘Oh, here we go, I’m out again’. So he was one of the next where I talked about him playing in that midfield and he just said, ‘Yeah, I’m happy to do it’.
“I thought he was excellent, I really did. There are areas of everybody’s game that we need to work on but he showed he has got that versatility.”
https://www.newsandstar.co.uk/sport/23995108.carlisle-united-boss-owen-moxons-fitness-cheltenham/