The 27-year-old was allegedly banished from first-team training at Forest last month and has been told that he is free to leave the club in the January transfer window.
McKenna moved to the City Ground in September 2020 from Aberdeen and helped the club secure promotion from the Championship in 2022.
The Scotland international, who has made a total of 105 appearances for Forest in all competitions, fractured his collarbone in April which ruled him out for the rest of the season.
McKenna has since failed to establish himself as a first-team regular at the City Ground this term having played in just five Premier League games.
All five top-flight outings took place in Forest's first five fixtures of the 2023-24 campaign, including his last in a 1-1 draw against Burnley on September 18.
McKenna has been tipped to return to his homeland in search of regular first-team football, with Sky Sports News reporting that both Celtic and Rangers are interested in signing the left-footed defender.
The report adds that McKenna could move to either club on an initial loan deal, with a view to signing on a free transfer in the summer when his contract at Forest expires on June 30.
It is understood that Celtic are currently in pole position to win the race for McKenna's signature, with Brendan Rodgers keen to bolster his defensive options this month.
Celtic are a man light in the centre-back department after Nat Phillips was recalled from his loan spell at Parkhead by parent club Liverpool earlier this week.
Phillips allegedly had the option to extend his temporary stay with Celtic, but the decision was made for him to return to Anfield after making just eight appearances in all competitions for the Hoops.
Cameron Carter-Vickers and Liam Scales have been the first-choice centre-back pairing for Rodgers so far this season, while Gustaf Lagerbielke, Maik Nawrocki and Stephen Welsh have also gain first-team minutes this term.
As for Rangers, Ben Davies is the only left-footed centre-back option at Philippe Clement's disposal, but he has only started four Premiership games so far this season, while Connor Goldson, John Souttar and Leon Balogun have featured more regularly at the back.