Liverpool goalkeeper Pepe Reina would welcome a return to Barcelona next summer.
Sheffield Wednesday chairman Milan Mandaric has confirmed Neil Warnock is on a five-man manager's shortlist.
Levein was "relieved of his duties" by the SFA on November 5 following a disappointing start to the World Cup qualifying campaign.
The SFA has confirmed Levein has now instructed his lawyers to serve a writ on the Association, who had offered to honour the remainder of his contract in full.
A statement from the SFA read: "Regrettably, the Scottish FA has received notification from lawyers representing Craig Levein that their client has served a writ on the Association.
"This notification has been received despite the Scottish FA's offer to honour Craig's contract in full, an offer that was made immediately upon the Board's decision to relieve Craig of his duties on November 5, 2012.
"The Scottish FA has since received notification that Craig has chosen to resign, thereby foregoing the offer made to honour his contract in full.
"In the notification received, failure to make a proposal in lieu of compensation has been cited.
"It is the view of the Scottish FA that no such offer is required given Craig's decision to resign, especially since an offer of mediation was rejected by his legal representatives.
"We will make no further comment at this time."
Levein had found himself under pressure after the Scots failed to record a single win from their opening four games of the current campaign.
Draws at home to Serbia and Macedonia, followed by defeats away to Wales and Belgium, left Scotland bottom of their group with little hope of booking their place at Brazil in 2014.
Those results ultimately sealed the fate of the former Hearts and Dundee United boss and his near-three-year tenure came to an end last month.
Under-21s boss Billy Stark was placed in interim charge while the SFA search for Levein's successor.