City are moving closer to unloading some fringe players to make room to freshen up the squad.
As it stands, City’s player wage bill is bordering on the 60 per cent limit of total income permitted for League One clubs. So the onus is on departures during the present transfer window before they can look to make additions.
Striker Connell has been limited to substitute roles and did not even get off the bench at Notts County as Parkinson threw on youngsters Oliver McBurnie and Ryan Clarkson.
With City well stocked for central defenders, Oliver is another touted to leave. The former player of the year has started only three times this season.
Parkinson also has a call to make on Matthew Bates, whose short-term contract expires after the Bristol City home game on Saturday.
Summer recruit Matt Taylor could even be considered surplus to requirements after failing to nail down a regular role. He has had just one 45-minute outing since returning from a successful loan spell with Colchester.
Andrew Davies is stepping up his recovery and should be back by the end of the month to bolster City’s defensive resources.
Parkinson said: “We’ve been working hard over the last three or four days. There have been a couple of calls to take our players, which I’m waiting to come back on.
“That will generate a bit of money which will help to get somebody the other way. We’re doing everything we can.
“A few of our lads need to go out and play and if they do move, that will free up some wages for us to bring one or two in.”
Reports that York were looking at Connell were dismissed by Nigel Worthington at the weekend and Parkinson confirmed: “We’ve not had any contact from them.”
The future of Nahki Wells remains the major talking point.
Championship club Reading are the latest side rumoured to be interested but reports linking him with Nottingham Forest appear unfounded.
Parkinson said he had heard nothing new on his top scorer, who hopes to recover from a tight hamstring to feature against Bristol City on Saturday.
He added: “The most important thing for Nahki is getting back out there and playing as well as he can. The rest takes care of itself.”
After Connor Ripley’s return to Middlesbrough, Parkinson intends to bring in a back-up goalkeeper this week and is casting an eye over Harrogate Town’s Craig MacGillivray.
The Skrill North stopper, who is 21 on Sunday, is training with City for the next couple of days.
Parkinson said: “He’s just one we are looking at. Lee Butler (City goalkeeping coach) has watched Craig a few times and this gives him a chance to train at a professional club.
“The goalkeeping situation is something I will definitely be resolving before Saturday’s game.”
Harrogate want a quick answer and insist City will have to pay as the former Stalybridge Celtic keeper is halfway through a two-year deal.
Boss Simon Weaver said: “It’s not going to be an extensive trial. They are going to have to make their mind up there and then.”