That is according to The Sun, who claim the Hammers are keen to land a replacement for Barcelona loanee Alex Song.
Carrick, who has also attracted interest from Premier League rivals Arsenal, is out of contract in the summer and is yet to open talks over a new deal.
According to Sky Sport Italia, the Greece defender's agent met with the Red Devils about a potential £24m deal - but he has no knowledge of the meeting.
But Manolas, who cost Roma £14m two years ago, insists he is unaware of any meeting, saying: "Manchester United? I know nothing, my agent tells me nothing.
GETTY
Kostas Manolas to evaluate future in the summer
GETTY
Arsenal to rival Manchester United for Joao Mario
"I have to be focused on Roma, I still have three years on my contract. After the end of the season we will look at things together with Roma."
Gunners manager Arsene Wenger is desperate to replace midfield trio Mathieu Flamini, Tomas Rosicky and Mikel Arteta and Mario, who has a £55m release clause, is said to be on his shortlist.
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