The 27-year-old was the standout player for an ordinary Betis side last season, netting seven goals and providing seven assists for the team who finished in the lower half of mid-table.
Fekir has been linked with a summer exit from the Seville-based club while his former club Olympique Lyonnais are entitled to 20 percent of any sale, while the player himself owns 10 percent of the economic rights, hence why Betis would need to sell for at least €30m to recover the reported €22m they spent last year.
Zenit are in the Champions League this year and are said to have turned their attention to the France international after discontinuing their interest in signing Christian Eriksen from Inter.
Betis pay Fekir a reported €7m gross in annual wages and could see his exit as a way to ease their financial pressures.
Los Verdiblancos missed out on European football for this season with Giovani Lo Celso, Pau Lopez and Junior Firpo were among those to depart last summer after a similar economic hit.