The Brazilian forward had missed Monday's 2-1 victory over Brentford because of a hip flexor problem, but the injury now appears less serious than first feared.
Manager Michael Carrick had already hinted that the issue was minor, and Cunha was back working with the squad at Carrington as preparations intensified for the visit of Arne Slot's side to Old Trafford.
Cunha has become an important figure for United in recent weeks. The former Wolverhampton Wanderers attacker scored the winning goal in the recent victory over Chelsea at Stamford Bridge, a result that strengthened United's push for UEFA Champions League qualification.
United followed that performance with another important win against Brentford, where goals from Casemiro and Benjamin Sesko secured three valuable points.
Cunha's return could prove crucial during the closing weeks of the campaign. The 26-year-old has produced four goal contributions in his last six league matches and has scored eight goals this season.
United are now closing in on a top-five finish and need only two more points from their remaining four league fixtures to guarantee a place in next season's Champions League.
Sunday's clash also gives United the chance to complete their first league double over Liverpool since 2016 after their impressive win at Anfield earlier in the season.
Carrick is expected to provide another update on Cunha's condition during Friday's pre-match press conference.
Bukayo Saka has said Arsenal would head into next week's Champions League semi-final second leg with confidence after securing a hard-fought draw away to Atlético Madrid in Spain.
Manchester United midfielder Kobbie Mainoo has signed a new long-term contract with the club after an impressive return to form under manager Michael Carrick.
Milos Kerkez says he is "growing" into life at Liverpool F.C. as he continues to adapt to the demands and responsibility of playing for one of England's biggest clubs.
Tottenham winger Xavi Simons has already begun his road to recovery after suffering a serious knee injury that will keep him out for several months.
