According to the Mirror, this will be the second battle between the two Manchester clubs following the Alexis Sanchez saga. The Chilean forward was at Arsenal and after failing to join Pep Guardiola's side in the summer, he was expected to complete a switch to the Etihad this month.
However, United were successful in beating their local rivals in bringing Sanchez to Old Trafford. The 20-time champions of England are set for anther transfer battle in signing the Ivory Coast international.
It is believed that both Jose Mourinho's side and City have made initial enquiries in signing Seri. He has a £35m ($50m) release clause in his contract with the Ligue 1 outfit. The two Premier League clubs are determined to secure his services in January as he is expected to leave before the end of this transfer window.
Mourinho added Nemanja Matic to the list of midfielders at United last summer. He now has the services of the Serbian international, Paul Pogba, Ander Herrera, Michael Carrick and Marouane Fellaini as the recognised midfielders in the squad.
Carrick will retire after the end of the season and join the Red Devils' backroom staff. In addition to this, the Belgium international will be a free agent in the summer and has so far not decided against signing a new deal.
City, on the other hand, are looking for a replacement for Yaya Toure. They have also identified Shakhtar Donetsk's Brazilian midfielder Fred as a long-term replacement for his compatriot Fernandinho.
Seri is not cup-tied for the Champions League and is one of the most sought after midfielders in Europe. A move from either United or City for the African star will see them include him in the European squad for the second-half of the season.