Saturday's printed copy of The Sun reported that the Whites are interested along with Wolves and Burnley.
Boss Dougie Freedman is unwilling to sanction a straight sale - but the report states Forest would consider letting Paterson go as part of a swap deal.
It does not state if there are any players belonging to the trio who Forest have their eye on.
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23-year-old Paterson was used mainly as a substitute last season, and has a deal at Forest at present taking him up until 2018.
Who should Forest look for?
Paterson is a talented but unproven prospect, and Forest would be getting a good deal if they were to demand former loanee Billy Sharp from Leeds United.
Sharp has in recent weeks been linked with a move to Sheffield United, as reported the Sheffield Star earlier this month and is could be available after failing to hold down a regular starting spot at Leeds last season.
With Forest in need of a goalkeeper, they could also look to Wolves former Manchester United man Tomas Kuszczak who is considered behind Carl Ikeme in the pecking order.
Perhaps most likely is a deal with Burnley, with the Nottingham Post reporting striker Lukas Jutkiewicz is wanted by the club, with Dougie Freedman working with him previously at Bolton Wanderers.