The former Liverpool captain left the club just a matter of months after making the switch to the Saudi Pro League, signing for the Dutch giants earlier this week.
In their hunt for a replacement, Al Ettifaq may seek to reunite Doucoure with his former Everton team mate Demarai Gray, who joined in the summer.
Fabrizio Romano claims that the club have made contact with Everton stating they would like to sign Doucoure this month, with them also believed to have reached out to Doucoure's camp.
Everton are thought to be disinterested in letting Doucoure leave, given his status as a key player in Sean Dyche's plans at Goodison Park.
Only injury has prevented the former Mali international from being ever-present this season, and his influence in the Everton midfield has been pivotal in the club staving off relegation in recent seasons.
After featuring against Aston Villa on his return from injury last weekend, Doucoure appears to have picked up another issue, and missed their FA Cup replay with Crystal Palace on Wednesday.
Doucoure's importance is illustrated by the remarkable statistic that Everton have won just four of the 35 matches he has missed since joining the club in 2020.
The Palace victory was also the first time Sean Dyche has won a match as Everton boss without Doucoure in the team at the eighth attempt.
Everton fans can take solace in the fact that Doucoure has frequently come out to offer his loyalty to the club, especially after he made himself unavailable for Africa Cup of Nations duty with Mali to focus on their battle against relegation.
Doucoure signed a new contract which will keep him at the club until 2025 back in November, and stated he wishes to stay in England for the rest of his career.
"I've never considered myself to play abroad. My wish was always to stay in England and at this club. I want to finish my career in England and this is my wish." Doucoure said after signing a new deal.
The lure of lucrative money from the Saudi Pro League has been tempting to many Premier League players over the past few months though.
Details of the financial incentives that may be offered by Al Ettifaq are not yet clear, but with Steven Gerrard's side down in eighth, nine games without a win, reinforcements may be sought quickly this month.