The 27-year-old has been heavily linked with a summer switch to join preferred club Real Madrid, but current boss Pep Guardiola could try to lure him to the Etihad when he takes charge of City.
Guardiola recently confirmed that he will leave the Bundesliga giants in the summer and sign for the Premier League club.
However, he admitted that he was not keen on raiding his former squad, but will only make a move if Real step up their chase for the Poland international.
United have been monitoring his situation over the past few months as they look to add more firepower into their attack, while Ligue 1 champions Paris Saint-Germain are also said to be keen.
Lewandowski is being linked with a £75m mega move to the Bernabeu after impressing with 33 goals in 32 appearances for club and country so far this term.