Diario Gol (h/t Luke Gardener of the Daily Star) reported the reigning champions of Spain and Europe could attempt to bolster their campaign with the swoop on Old Trafford and might also target the signings of Alexis Sanchez of Arsenal and versatile Liverpool player Emre Can.
Ibrahimovic suffered a serious knee injury at the end of last season, but the mercurial Swede was a huge success as United stormed to triumph in the EFL Cup and UEFA Europa League.
Per Alec Shilton of The Sun, United manager Jose Mourinho revealed Ibrahimovic is closing in on a return to the first team:
"We have the group of players which are the ones that we hope will recover as soon as possible.
"They have to work every day but they are in a good position now. [Paul] Pogba, Ibrahimovic, [Marcos] Rojo, [Marouane] Fellaini.
"They are in good positions so I think we can go into this part of the season, the Christmas period, and after, in a strong position."
Ibrahimovic hit 22 goals in 39 appearances in the Premier League and Europe last season, according to WhoScored.com, before injury cruelly ended his campaign prematurely.
The player confirmed he would extend his stay in Manchester last August:
It is unlikely Mourinho will allow Ibrahimovic to leave United, especially for a direct rival for the UEFA Champions League.
United lack potential No. 9's at present, and the Swede will be back in the starting XI if Romelu Lukaku is injured at any point.
Despite his recent major injury, Ibrahimovic is known for his fitness and conditioning, and he could be vital for the Red Devils' trophy charge in the second half of the campaign.
In other United news, Marouane Fellaini has reportedly held talks with Mourinho, with the coach wanting the 29-year-old to remain at the Theatre of Dreams next term.
Per Sean Kearns of Metro, Fellaini has attracted significant interest from abroad as his deal runs out at United in the summer. The Belgian international is being chased by Turkish and Chinese teams, prompting Mourinho to hold talks with the midfielder. Fellaini is on £80,000 a week at United, and if a new deal cannot be agreed, the player would command a potential £18 million price tag in January.
It is unlikely Mourinho will cash in on the 29-year-old in the winter, with Fellaini adding brawn to the manager's selection.
Fellaini has also won over a number of his doubters in the United crowd, with the Stretford End singing his name through the season.
The Belgian will never be the most cultured footballer at United, but his effort and goal threat make him a valuable member of the wider squad.