The Toffees have won just one of their last seven matches away from Goodison Park and could come unstuck against the Lions, who have lost just one of their last 11 FA Cup clashes on home soil.
Furthermore, Neil Harris' men are unbeaten in their last eight matches on their own patch in this competition and so the stage is set for a fascinating fourth round fixture on Saturday evening.
Millwall have won their last four home FA Cup ties against Premier League opposition and SportPesa's 7/2 (4.50) quote for Harris' men to beat the Toffees may attract support.
Marco Silva's side are a 5/7 (1.71) chance with SportPesa to secure their place in the fifth round inside 90 minutes whilst the same firm go 27/10 (3.70) that a replay at Goodison Park is required to settle this tie.
The Lions are at full-strength. Shane Ferguson, who scored twice after coming on as a substitute in the previous round, is pushing for a start and veteran striker, Steve Morison, will also hope to play his part for the hosts.
Everton fielded a strong, albeit not full-strength, side in the previous round. Silva will likely take a similar approach on this occasion which could mean starts for Ademola Lookman, Yerry Mina and Jonjoe Kenny.
There have been at least three goals scored inside normal time in eight of Everton's last 10 FA Cup away matches and furthermore, there have been more than two goals in five of Millwall's last seven home ties in this competition.
Millwall have scored in their last 11 FA Cup home ties and Everton have found the net in all but one of their last 14 away matches in this competition.
Value, then, could lie in backing at least three goals - and both teams to score. The 5/4 (2.25) shot from SportPesa could provide punters with a path to profit on Saturday evening.