The defender has made just one Premier League appearance for the Villains.
The Mail reports that the 29-year-old looks destined to leave the Championship side in the coming months despite only joining the club last year for £500,000.
However, news of his seemingly imminent departure will come as little surprise to most Villa fans. Crespo made just one appearance in the Premier League before joining Spanish side Rayo Vallecano in January on loan for the rest of the campaign.
And while the Mail reports that he will return to his parent club for the start of pre-season, they also state that it is highly unlikely that he will be a part of Roberto Di Matteo's squad when the new campaign gets underway.
Should PAOK's interest lead to an offer, it arguably seems doubtful that Crespo will have much hesitation when it comes to moving on, unless he has to consider other bids that are put on the table from elsewhere.
The team have secured a place in the third qualifying round of next season's Champions League, so would arguably be an excellent option for the Spaniard following his failure to make any kind of impact during Villa's hugely disappointing campaign.