Spurs are back above their north London rivals after a late 2-1 win at Stoke on Sunday but they can be leapfrogged by the Gunners if Arsene Wenger's men see off relegation-threatened Wigan this week.
However, AVB believes the FA Cup winners can cause an upset and take the battle for a top-four place down to the final game of the season this Sunday.
"The dream is still alive for us," the Tottenham manager said. "It's not down to us anymore but we still want to take it to the last day when we play at home and Arsenal are away.
"It was an extremely important victory (at Stoke) for us because it keeps us in the frame."
Villas-Boas is now hoping Wigan, fresh from their stunning FA Cup final triumph on Saturday, can do them a big favour on Tuesday.
"What we will see is a Wigan side who are very motivated," he added. "They will give Arsenal a hard game. I expect a competitive match. You never know."