While the feisty forward and his Steelers' club have yet to cement a contract for the 2022-23 season, the club's head strength and conditioning coach Mike Mawes is monitoring every phase of the skater's recovery from an anterior cruciate ligament tear suffered against Aalborg Pirates in the team's first Continental Cup game in Denmark, last November.
And whatever north America-based Connolly's EIHL employment status will be, come August, Mawes is aiming for him to be fit and ready to go.
"I have been working with Conns since having his ACL surgery and he has been making some good progress" said Mawes.
"Obviously working with Conns remotely is more challenging than face-to-face coaching but it is something I have a lot of experience in doing.
"Conns' programmes generally last from 4-6 weeks in length, they are dependent on progress and how his knee is tolerating the new working loads and exercises.
"Each programme is provided with a detailed overview of how, why and what we are looking to achieve.
"The exercises prescribed are sent through with a video demonstration, so Conns knows what we are expecting to see.
"Aside from the programme, we have frequent catch-ups over the phone to monitor progress and to make any changes necessary."
Mawes says recovery from the injury - one that Maltby's Liam Kirk has endured - is never a speedy one, whether a player is 36 like Connolly or younger.
"Recovering from an ACL injury unfortunately isn’t a quick fix, it can take around nine months but, in some cases, individuals can return to their sport quicker if rehabilitation goes well.
"There are multiple steps that need to be completed before returning to sport after and ACL injury.
"With Conns, he started strengthening and improving the function of his injured knee before surgery, so he was in a better start position post-op."
Mawes added that recovery and strengthening processes are broken down into multiple phases.
"Each phase has a different focus from range-of-motion, stability, strengthening the injured side, trying to limit any muscular imbalances, returning to low-level, jump-based work to running and changing direction then eventually skating then full practice.
"Rehabilitation from an injury like an ACL reconstruction can get very tedious but with an athlete like Conns he is all in, a true professional.
"His age isn’t something I am overly concerned about; he looks after himself and is following guidance from myself and the physio so I am confident he will return to match fitness.
"The goal is to get him game ready by August. Obviously, we have a way to go and we hope for no setbacks."
Connolly's attitude on the ice - and his 222-game experience in the EIHL - makes him a priority signing for Sheffield, should his fitness be 100 per cent again.