According to the report, the two Scottish clubs are in talks over the transfer of the Scotland international.
It has been further reported by The Scottish Sun that Celtic manager Rodgers does not see Mackay-Steven as part of his immediate plans.
Gary Mackay Steven celebrates
However, the former Liverpool boss has dismissed speculation that the 25-year-old winger will leave Celtic this summer.
BR on if @Gary__11 is going out on loan: "Not that I'm aware of. Still injured. Nothing in that." (MH)— Celtic Football Club (@celticfc) August 5, 2016
Rodgers has also given his thoughts on the current situation of Charlie Mulgrew.
Mulgrew, whose contract with Celtic ended at the end of last season, is training with the Bhoys.
The future of the 30-year-old, who is a very versatile footballer and can play as centre-back, left-back or central midfielder, is uncertain.
Charlie Mulgrew scores for Celtic
"His contract was up, he was looking to negotiate with the club and unfortunately those negotiations stalled,” Rodgers told The Scottish Sun about Mulgrew.
"He's without a club and he asked if he could come in and train for a few weeks until something happened further down the line.
"By all accounts, he's a good guy, and from speaking to him a few times, he's a good guy who wants to work and train well. He's been a good servant to Celtic here and I have no problem in helping out good people like him."
Celtic will kick off their 2016-17 Scottish Premiership campaign with an away game against Heart of Midlothian on Sunday.