The U’s have been linked with the 21-year-old, who submitted a transfer request last week.
Fellow Sky Bet Championship sides Hull City and Luton Town have reportedly made bids of £2.5 million for Kamara, with his preference being the Tigers according to BBC Sport.
United are understood to have bid for Kamara, however it is unknown at this stage whether that offer matched the ones made by Hull and Luton.
This newspaper understands that the U’s have other options though, if a move for Kamara fails to materialise.
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Kamara spent last season on loan at Portsmouth, and the Fratton Park outfit have also reportedly shown interest in signing their former loanee on a permanent basis.
Kamara came through the Canaries academy, and made his senior debut in April 2023.
He joined Pompey on loan for the 2023/24 campaign, and scored 10 goals in 52 appearances across all competitions, as John Mousinho led the side to the League One title.
Since returning to Carrow Road this summer, he has made three appearances this season, including as a substitute in the Canaries’ 2-0 defeat at United earlier this month.
He opened the scoring in a 4-3 win against Stevenage in the first round of the Carabao Cup.