The 53-year-old is expected to fail in his efforts to earn a new contract as the demanding Whites' owner Massimo Cellino looks set to sack his sixth manager in just two years at Elland Road (The Mirror).
Evans has done a good job at Leeds since replacing Uwe Rosler in October, securing a 13th-placed Championship finish when his remit was to avoid relegation - they finished 19 points clear of the bottom three.
But he might well be on the job hunt very shortly and Sky Bet have installed him as 6/4 favourite to take charge at the City Ground by the start of next season.
The news has not gone down well on social media, with a number of Forest fans expressing some pretty frank views with regard to the former Rotherham United boss.
Steve Evans is hot favourite for the #nffc job. Exactly the sort of ridiculous decision Fawaz would come up with.— Danny Stewart (@DannyPStewart) May 10, 2016
Hope the Steve Evans rumours to Forest are just that. But then who is craziest to take it #nffc— Mark C (@markyc07) May 9, 2016
Don't worry about Steve Evans being odds-on. Poyet was, and MON was almost evens at one point. Means nothing. #nffc— Hannah Dexter (@hannahforest) May 9, 2016
Can I start the "we don't want Steve Evans" petition. For good of our club retweet and like if you agree #NFFC— Stuart (@REDSTU1986) May 9, 2016
If Steve Evans become #nffc manager, I'll demand a refund on my season ticket.— Richard Lenton (@Leno_17) May 9, 2016
#nffc Steve Evans ? Would rather have Platt back with Davies as his No2 .— @clashcityrocker (@nffc2009) May 9, 2016
whoever the next manager of #nffc is we all need to get behind him. imagine we could all get behind Steve Evans and nobody would see us.— @Giuseppe_Timone (@_mrjoey) May 9, 2016
I've said it before and i'll say it again, ANYONE BUT STEVE EVANS ... #nffc— Sam (@Sam_Rowan) May 9, 2016
Gus Poyet had previously been favourite, but the former Sunderland manager has since taken the Real Betis job in Spain.
Paul Williams has been managing Forest in a caretaker capacity since Dougie Freedman was sacked in the middle of March. Forest, who beat MK Dons 2-1 on the final day of the season, finished 16th.