Forshaw has been on the fringes of Boro’s first team this term and is yet to feature since Tony Pulis replaced Garry Monk in the dugout.
Championship promotion-contenders Derby County and struggling Sunderland are also monitoring the 26-year-old’s availability, according to the Northern Echo.
The Black Cats are also interested in a move for Forshaw’s team-mate Adam Clayton.
Forshaw and Clayton are likely to start Middlesbrough’s FA Cup Tees-Wear derby against Sunderland on Saturday, with Pulis expected to ring the changes.
Pulis is due to hold talks with Boro chairman Steve Gibson next week to discuss possible exits.
The 60-year-old believes the squad he inherited from Monk is bloated and needs trimming down.
The Northern Echo claim Pulis hopes to axe up to five players this month.
Forshaw came through the ranks at Everton before moving to Brentford in 2012 following a successful loan spell.
The Liverpool-born ace spent six months at Wigan before penning a three-and-a-half-year deal with Middlesbrough in January 2015.
The Riverside Stadium has been a hive of activity this week.
Connor Roberts was sent back to parent club Swansea after his loan deal was terminated while Connor Ripley and Matty Elsdon returned from Burton Albion and Inverness respectively.