The 38-year-old said on national TV show in Argentina that he would no longer play professionally.
Ronaldo, his country's record goal-scorer, came on in the 62nd minute but failed to find the net as a late Ricardo Horta strike salvaged a 1-1 draw for Portugal against Spain in the Nations League.
BCCI president and former Indian cricket team captain Sourav Ganguly, who is facilitating the deal, told media that negotiations are on with the 'Red Devils' and a few others and a clear picture will emerge in about two weeks.
The defeat means it is now mathematically impossible for sixth-placed United to qualify for the Champions League, as they sit five points adrift of fourth-placed Arsenal with one game left to play.
Rangnick, who will make way at United for Erik ten Hag at the end of the season, has said he will also stay on in a consultancy role at the Premier League club.
Greenwood remains suspended by Manchester United until further notice.
Ronaldo's 62nd-minute strike was his 17th league goal this season with only Mohamed Salah of Liverpool having found the target more often.
The Portuguese superstar's goal wasn't enough for United as Arsenal ran out 3-1 winners at the Emirates.
United has been led by interim managers Michael Carrick and currently Ralf Rangnick since Ole Gunnar Solskjaer was fired in November.
Cristiano Ronaldo received an outpouring of solidarity from Manchester United fans and their Liverpool counterparts during a Premier League match he missed after the death of one of his new-born twins.