The 28-year-old, who moved to Old Trafford in 2010, has held talks over a new deal but is yet to commit himself to United beyond next summer.
His deal is set to expire at the end of the season, however the 'Red Devils' have a contract extension clause written in to his deal.
And according to 'The Sun', Everton are set to swoop and hopefully sign the 28-year-old on a pre-contract, paying no transfer fee.
Silva is on the lookout for another central defender with captain Phil Jagielka approaching the end of his career and Kurt Zouma's loan from Chelsea expiring at the end of the season.
It is understood that Everton are willing to match Smalling's £90,000-a-week deal at Old Trafford, with Marco Silva's side aiming for European qualification.
The 'Sun' also understand that Everton will make an approach for Smalling in January, if they are unable to secure his services on a free transfer.