The 31-year-old striker has caught the eye during his loan spell at United from Shanghai Shenhua, scoring five times for the club.
The Nigerian signed a deal to stay at United until January, but, PSG are considering him as an option as they look to replace Edinson Cavani.
PSG Sporting Director, Leonardo Nascimento de Araújo, has drawn up a shortlist of possible targets and will even explore the possibility of signing Cristiano Ronaldo amid rumours Juventus are looking to get him off their wage bill.
However, French publication Foot Mercato claim that PSG have also made contact with Ighalo’s representatives about a possible transfer.
The French champions splashed out £52million to sign Mauro Icardi on a permanent basis earlier this summer but are looking for another attacking player to provide competition.
19-year-old Arnaud Kalimuendo has been integrated into the first-team squad ahead of next season but PSG want to bring in a more experienced and reliable player.
Ighalo fits that mould and would be a much cheaper option than some of PSG’s other targets.
Cavani, meanwhile, is still searching for a new club after seven-year spell at the club came to an end last month.
Newly-promoted Leeds were in the race to sign the 33-year-old Uruguayan but now face an uphill task to get a deal over the line with Bayern Munich and Benfica the current favourites to land his signature.