Press Association Sport understands that no fee has yet been agreed between the clubs, but that discussions have progressed and there is an appetite to do a deal, meaning the 30-year-old could be on his way to Teesside within days.
Downing has been left out of the Hammers squad for their Europa League clash with Birkirkara on Thursday evening.
Boro have been in talks with the Hammers for some time over their former Academy graduate, who left the club for Aston Villa in a £12million switch in July 2009.
It appears he is surplus to requirements under new boss Slaven Bilic and despite interest from other suitors, including Barclays Premier League club Sunderland - with whom Downing had a loan spell earlier in his career - the Riverside seems to be his preferred destination.
Head coach Aitor Karanka and his players are currently training in Marbella with the club's medical staff on hand, meaning there could be delay in processing medical checks before a transfer could be completed
Source : PA
Source: PA