QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
Ilkay Gundogan has commited his future to Borussia Dortmund by signing a new contract.
The 39-year-old's departure was confirmed in a short statement on their official website and brought to an end his long association with the Dark Blues.
Smith captained the club and made 400 appearances as a player before returning to Dens Park as first team manager.
He also guided the club through their 2010-11 campaign - dubbed the 'Dee-Fiant' season - after Dundee retained their place in the Irn-Bru First Division despite a 25-point deduction for a second descent into administration.
However, results this season have left the club rooted to the bottom of the Clydesdale Bank Premier League, 15 points behind nearest rivals St Mirren.
Asked how tough a decision it was to part company with Smith, Dundee chief executive Scot Gardiner told Sky Sports News: "It was extremely difficult.
"It would be extremely difficult for anyone who knows anything about Dundee.
"The word legend is too often bandied about but he has been here for 17 years, through two administrations, coached the club, played for the club, captained the club, led it out at Hampden.
"He brought 'Dee-Fiance' after a 25-point deduction. Outrageous and amazing things.
"However football is a very cruel game."
The club statement read: "Dundee FC today announced that they have parted company with manager Barry Smith with immediate effect.
"Until matters regarding this have been formally concluded, no further statement will be made."
Dundee look set for a quick return to the First Division, following their hasty promotion to the SPL.
They were late additions to the top flight in the summer, after replacing Rangers, and have struggled to compete throughout the campaign.
Smith's future came under scrutiny in early January, with reports suggesting his position would be discussed by the club's directors.
He then appeared to receive the backing of the board, who acknowledged the difficult task he has faced this term, while vowing to boost their survival bid by adding new players before the transfer deadline.
David Morgan was signed on loan from Nottingham Forest and former fans' favourite Gary Harkins also returned to Dens Park.
But results failed to improve and the SPL strugglers have not registered a single victory in their last 12 league outings.
Club chiefs now begin the search for a new manager, with Dundee facing a daunting trip to Celtic Park to face the league leaders on Sunday.
Former Dunfermline and Aberdeen boss Jimmy Calderwood has emerged as an early favourite with bookmakers for the hotseat.