The Dutch side, coached by Giovanni van Bronckhorst, are seeking additional attacking cover in case they lose a forward before the window closes, with Feyenoord's participation in this season's Champions League adding to the appeal of a move for the 18-year-old.
Obi, a Denmark Under-21 international, had previously attracted interest from Bundesliga side 1. FC Köln earlier in the window, though a switch to Feyenoord would offer a higher level of European competition.
The teenager has made eight senior appearances for Manchester United since arriving from Arsenal in 2024, including becoming the youngest player to start a Premier League match for the club when he featured against Brentford last season, but manager Michael Carrick has not included him in his plans following a mixed pre-season.
United are understood to be open to a loan exit that would allow Obi-Martin regular first-team football at a higher level than he could currently expect at Old Trafford, with the club having previously stated a preference for sending the striker to continental Europe rather than arranging an in-division loan within the Premier League.
Feyenoord's interest comes amid uncertainty over their own forward line heading into the closing days of the window, with the Rotterdam club keen to ensure they are not left short of attacking options regardless of what departures may follow elsewhere in their squad.
Should the move proceed, Obi would have the opportunity to make his continental debut in the Champions League, a significant step up in profile for a player still just 18 years old.
Obi arrived at Old Trafford after turning down a scholarship offer from Arsenal, where he had built a reputation as one of the most prolific young forwards in English academy football, having once scored ten goals in a single youth fixture against Liverpool.
His development has continued steadily since the move, with a spate of first-team injuries in United's forward line during the 2024-25 season handing him unexpected senior opportunities earlier than might otherwise have been the case, though sustained progress now appears to depend on finding regular football away from Old Trafford this season.