The Kenyan captain came on as a second half substitute as Spurs lost 2-1 to Liverpool in a Premier League match on Saturday, and has been included the squad that travelled for the Champions League opener in Italy.
Wanyama had not featured for Tottenham before Saturday's defeat at Wembley after recurring a knee injury during pre-season but could be in line for his first start if manager Maurico Pochettino feels Eric Dier needs a rest.
Spurs travel to the San Siro after back-to-back Premier League defeats at the hands of Watford and Liverpool. Pochettino knows a defeat to the Serie A giants could be costly, with Barcelona and PSV Eindhoven the other teams in a tough Group.
Spurs have taken a depleted squad to Italy with Toby Alderweireld and Kieran Trippier left behind in London in order to rest while skipper Hugo Lloris and midfielders Dele Alli and Moussa Sissoko are out through injury.