The 28-year-old has become a huge favourite at the City Ground, amongst teammates as well as Forest supporters, particularly after playing a pivotal role in the penalty shootout victory over Sheffield United in their playoff semi-final back in May.
The Reds would then go on to beat Huddersfield Town 1-0 in the Championship playoff final at Wembley, ending their 23-year wait for a return to the Premier League.
Ahead of the 2022-23 campaign, Forest have offered Samba fresh terms to extend his stay in the East Midlands, with just 12 months remaining on his current deal.
However, according to The Athletic, the shot stopper has deemed the proposal unacceptable and rejected the offer, before revealing his desire to leave the club during the upcoming transfer window.
The report outlines how Samba's decision is not said to be financially motivated, but that Forest, and manager Steve Cooper, remain confident of changing his mind this summer.
The newly-promoted outfit face the decision of selling Samba in the coming weeks in order to demand a transfer fee, or risk losing the goalkeeper on a free upon the expiration of his contract in June 2023.
Meanwhile, Cooper was said to be on the look out for a new goalkeeper to provide competition to Samba ahead of their return to the Premier League, with an interest said to be held in Burley's Nick Pope following their relegation from the top flight.