Boro took the Toffees to extra time at Goodison Park in the Capital One Cup earlier this season and will welcome Roberto Martinez, who lifted the FA Cup with Wigan last season, and his side to Broadhall Way at the end of January.
"It won't be easy to play against the cup-holding manager or his excellent Everton team. They have some outstanding talent. A cup-holding manager doesn't loosen his grip lightly in my experience," Westley told Boro's website.
"We tested ourselves against them at Goodison Park and came up just short over 120 minutes; that will be good for our confidence but is unlikely to generate complacency on their part.
"The positive is that we will probably be stronger than we were at Goodison, with new signings on board and big players back from injury.
"The only FA Cup question we need to focus on now is 'how do we win'? That is a tough question to answer, but there is an answer to any question if you look hard enough and we will certainly not be intimidated by the challenge, tough though it is."