The former England boss is among the leading candidates for the Goodison Park job after Ronald Koeman was sacked last month — and is reportedly due to meet Everton chiefs in London on Wednesday to discuss the role.
Part of his severance agreement saw Palace insert a clause stating they would be due compensation were he to step into any club job before a certain date — which is understood to be next July.
Sam Allardyce has admitted he would consider the Everton manager's job if he was offered it
Allardyce has been out of football since helping Crystal Palace avoid relegation last season
At the time of quitting Selhurst Park, Allardyce insisted it was because he needed a break from management but he could now be set for a sensational return to club football.
The former Porto and Valencia boss has enjoyed a stunning start to his tenure at Molineux and guided them to a 2-0 victory over Norwich on Tuesday night.
And it is understood his performances have not gone unnoticed, with the Toffees taking note as they continue their search for Koeman's replacement.
According to Sky Sports' Spanish football expert Guillem Balague, Nuno is one of the contenders for the Goodison Park job.
He wrote on Twitter: 'Everton have contacted Nuno as one of the potential candidates to replace Koeman.
Wolves boss Nuno has emerged as a shock candidate for the Everton managerial vacancy
The former Porto manager has enjoyed a stunning start to his tenure in the Championship
'His agent Jorge Mendes is listening, no decision made yet.'
Nuno was appointed as Wolves boss on a three-year deal last May after managerial roles at Rio Ave, Valencia and Porto.
He was heavily backed in the transfer market and he has been rewarded, leading Wolves to 10 wins in their 15 league matches this season.
But he could now make the jump to the Premier League, with 18th-place Everton looking for a new manager to spearhead their climb up the table.
Allardyce has previously stated his interest in becoming the Toffees' next manager and would relish the chance to 'put the team back together'.
Nuno has experience of managing in the Champions League with Valencia and Porto
Everton – who lost 2-0 to Leicester – are currently in a relegation battle, sitting 18th in the table
Everton are continuing to take their time in finding Koeman's permanent successor and David Unsworth will see out the next two games before the international break.
Allardyce has had opportunities to go back to work since leaving Crystal Palace earlier this year but none have had the appeal of Everton.
They are in the bottom three after a dreadful start to the campaign but Allardyce believes he has the expertise to take them away from trouble.
'Who knows? I'd have to consider that, if that phone call happens, said Allardyce. 'There's no point in speculating at the moment, David Unsworth is in the chair.
'Joe (Royle) sat upstairs will have an opinion but at the moment it looks like it's really going to be tough for Everton to get out of that position.'
Burnley boss Sean Dyche has swatted away any suggestion his mind is on the Everton job