Aston Villa and Norwich City are both also claimed to be interested.
The former Leeds United centre-back has been in good form this season for the Owls, and impressed in a high profile Capital One Cup victory over Arsenal, in which his side kept a clean sheet.
The Mirror report Norwich City and Aston Villa are also interested in Lees, with the Canaries holding a potential key to a deal, with Michael Turner and Gary Hooper currently on loan.
The paper's report claims Lees is valued at around £7 million, and Newcastle are particularly keen to test Wednesday's resolve to keep him.
Sunderland sit in the Premier League relegation zone, with Newcastle one place out in 17th. Signing Tom Lees would certainly help out either club, but the defender will want to consider his options carefully.
Even though they could make a big profit on Lees, Sheffield Wednesday do not need to sell, taken over by rich owner Dejphon Chansiri earlier this year. The club are hoping to get promoted this season, and currently sit ninth, just four points back from the play-offs. Lees will not want to make the wrong move, and end up in the Championship next season with the Owls in the Premier League.
Lees is a former England under-21 international and left Leeds United in the summer of 2014 after a series of poor performances, and has gone onto transform his prospects with consistent displays for Sheffield Wednesday. He currently has a year-and-a-half remaining on his contract.
Newcastle saw Lees' talents first hand earlier this season, when he helped the Owls to a 1-0 Capital One Cup win at St James Park.