The 22-year-old World Cup hopeful has not featured for the first team since suffering a hamstring injury against West Ham on December 15, but has recently stepped up his rehabilitation, part of which included a run-out for the Under-21s, and so is likely to be back in contention this weekend.
"We are positive on Andros and he has a chance (for Everton), he is up for selection and is champing at the bit to return," Sherwood said on the club's official website, www.tottenhamhotspur.com.
Sherwood confirmed midfielder Mousa Dembele should also be available after missing the draw with Hull because of an ankle injury.
Tottenham are in fifth place, a point behind Everton, who beat Aston Villa last weekend.
Defender Jan Vertonghen and Younes Kaboul are two more of Sherwood's players to recover full match fitness following lay-off from respective ankle and thigh problems.
Captain Michael Dawson has welcomed the competition for places that such strength in depth of numbers brings as Spurs look to secure a top-four Premier League finish and also make progress in Europe.
"It is always good to have players back. We have the Europa League starting again soon as well, so there are plenty of games," Dawson said.
"We have top players who want to play, so competition is high and you know you have to perform well to stay in the team.
"We all want the game time and we are all pushing each other."
Sherwood took over when Portuguese head coach Andre Villas-Boas was axed in December and has guided the team to five league wins since being promoted from the backroom staff.
Veteran keeper Brad Friedel, likely to be utilised again for the upcoming European tie against Ukrainian outfit Dnipro, feels the 45-year-old's time working under previous Spurs managers has helped make for a smooth transition.
"Like [Sherwood] said when he first got appointed, there wasn't this big settling in period for him because he's been at Tottenham for so many years and he knows the players," Friedel told talkSPORT.
"We have had a lot of very good training sessions to understand his style of football and what he wants to implement, and a lot of the players who didn't know him now know his demeanour and what he wants, so it is all good so far."