The 26-year-old Galatasaray centre back has been a top target for Villa boss Dean Smith for some time due to his consistent performances in Turkish Football.
The DR Congo international looked all set to move to Villa Park in January but the move was scuppered due to an injury. Luyindama is understood to be keen on the Villa move but it remains to be seen whether he will be swayed by interest from Goodison.
Everton looking to bolster defence this summer
The record-breaking Turkish champions are desperate to keep hold of the player however, it is understood that a fee as little as £11million would be enough for either Everton or Villa to complete the transfer.
Luyindama has only been plying his trade in Istanbul since last January having joined on loan from Standard Liege before making the move.
The Toffees have made no secret that they're wanting to strengthen at the back this summer. The club have also made an official bid for Barcelona defender Jean-Clair Modibo, who has spent the second half of the season with Schalke.