The 34-year-old joined Real Madrid on loan from Espanyol last summer and has scored 14 goals in 38 appearances this season.
Madrid have the option to make the deal permanent for €1.5 million (£1.2m) this summer as part of their loan agreement with Espanyol, who are pushing for promotion back to La Liga this season.
United, meanwhile, are keen to sign a striker at the end of the season having been unable to bolster Erik ten Hag’s attacking options in the January window.
According to Relevo, United’s hierarchy have made an initial approach for Joselu to gauge his situation and potential transfer fee for the summer transfer window.
Speaking about his future last week, the former Stoke City and Newcastle United forward made it clear that his preference is to remain at Madrid.
‘I hope to stay with Real Madrid on a permanent deal,’ Joselu told ABC.
‘I had a clause that if Espanyol went down, I could go out on loan. And well, Madrid had the opportunity, they thought it was convenient to be able to trigger it. And here I am.
‘Well, there’s a contract, an option to buy, Madrid can buy me in the summer. There are many situations, if Espanyol do not get promoted, if they do go up. A lot of things that can happen.’
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