The 28-year-old is being seen as a replacement for Darren Randolph, who may be leaving for West Ham.
If the Hammers put in a big offer for Randolph, then Boro will look to the Rangers shot stopper as their new number one.
West Ham want to sign Randolph to offer competition to their first choice keeper Lukasz Fabianski.
The news comes out of the Daily Mail.
Foderingham has played four times this season, keeping a clean sheet in three of those appearances.