The 35-year-old joined United on a year-long contract from Paris St Germain before the 2016-17 campaign and was vital to their League Cup and Europa League triumphs.
He scored 28 goals in 46 appearances before sustaining a season-ending knee injury in April that could keep him out until next year.
Ibrahimovic, who underwent surgery in May and will be out of contract on June 30, was the only player on United's release list.
The Premier League said on their website (www.premierleague.com) that the information was correct as of May 29, but a player's status could have changed since that date.
The BBC reported that the Swede would remain in Manchester to continue his rehabilitation at the Carrington training ground.
His agent Mino Raiola said last week that Ibrahimovic would hold talks with United to extend his stay despite receiving offers from other clubs.
"He wants to stay in England, he wants to stay at the top and if he sees that he can be a valuable asset for Manchester United, then why not Manchester United?" Raiola told British radio broadcaster TalkSPORT.
"He can be a valuable asset for some other top clubs also. But I think it is respectful to talk to Manchester United and to see what all parties want."
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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