The Portuguese is heavily expected to replace Louis van Gaal at Manchester United.
The Bees finished ninth in the Championship and Smith hopes his side can make further progress next season.
Leon Osman, Steven Pienaar, Tony Hibbert and Darron Gibson are all out of contract at Everton this summer.
Newcastle United are currently the favourites to win next season's Championship.
Former Rotherham United boss Neil Warnock is reportedly on Nottingham Forest's shortlist.
Kevin Wimmer has made 10 Premier League appearances for Tottenham Hotspur this season.
Mark Warburton's Glasgow Rangers side were beaten 3-2 by Hibernian in the Scottish Cup final yesterday.
The Arsenal defender has been linked to both Barcelona and Bayern Munich.
How we rated the Villa players after a dismal season saw the club's 28-year stay in the top-flight come to an end.
Liverpool ran out of steam in their recent Europa League final defeat.
Could Manchester United have hinted that they will wait until the summer to bring in a new striker.
Jamie Carragher is worried about a potential Everton v Liverpool derby in the Capital One Cup.
The Tottenham Hotspur boss has taken his side forward after a season and a half. Where will the Reds be once their manager has had as much time?