The former Manchester City and Liverpool striker left Italian club Brescia following their relegation from Serie A.
A switch to Brazilian side Flamengo or Italian lower-league minnows Como has been touted but he could have a fresh shot at the Champions League with the Liga I champions.
Romanian outlet gsp have claimed Cluj, who are coached by Chelsea legend Dan Petrescu, have held advanced talks with the 29-year-old.
Owner Nelutu Varga told local media that he had two major transfer targets in Slavia Prague winger Nicolae Stanciu and a “top Italian striker.”
The businessman added: “This will be a real coup for Romanian football.”
Sources confirmed to Cluj TV station Look Sport that the unnamed player is indeed Balotelli.
Transylvania-based Cluj clinched their third consecutive title on Monday with a 3-1 win at Universitatea Craiova, and will enter the Champions League at the first qualifying round.
Petrescu’s side fell at the final hurdle of the current season’s qualifiers after beating Celtic, then knocking Lazio and Rennes out of the Europa League before an away goals defeat to Sevilla in the last-32.
Balotelli won the Premier League and FA Cup in his three-year spell with City before leaving for AC Milan in 2013.
A triumphant homecoming to Brescia last summer did not go to plan.
Scoring just five goals in 19 games for his local side, the striker encountered a number of racist abuse episodes and did not play at all after the coronavirus shutdown.
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