Ibrahimovic has scored 27 goals in all competitions in his debut Premier League season.
The former Juventus, Inter Milan, Barcelona, AC and Paris Saint-Germain striker will leave big boots to fill.
But Lewandowski, 28, is seen as the perfect fit.
The Pole has 44 goals to his name this season for club and country.
Robert Lewandowski has been prolific for Bayern Munich this season and is seen as the perfect fit for Manchester UnitedEPAPoland hitman Robert Lewandowski is physically imposing as well as technically giftedReutersJose Mourinho reportedly will move for Robert Lewandowski if Zlatan Ibrahimovic does not renew his Manchester United contractAP:Associated Press
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Lewandowski possesses the same target-man type qualities Mourinho favours in a striker.
He has played as the lone forward for both Borussia Dortmund and Bayern, where he has consistently proven himself.
But United's hopes of landing Lewandowski rest on whether they secure Champions League football.
The Red Devils are sixth in the table and four points off fourth-placed Manchester City with a game in hand.
Zlatan Ibrahimovic has scored 27 goals in all competitions for Manchester United this seasonPA:Press AssociationAntoine Griezmann is also on Jose Mourinho's transfer wishlist this summerEPA
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