The midfielder is currently without a club after leaving Nottingham Forest at the end of last season following the expiry of his contract.
Lingard has asked for a month's trial having been keen on a move to Saudi Arabia all summer.
Al-Ettifaq boss Steven Gerrard is keen to sign the player, providing everything goes to plan.
talkSPORT understands the 30-year-old is looking for around £7million-per-year [€8m], however, there is work to do with Ettifaq's budget being closer to £4.35m [€5m].
Lingard, who spent his entire career at Manchester United until 2022, had been training with West Ham during recent months with suggestions that he could move to East London.
The attacking midfielder scored nine goals in 16 appearances for the Hammers during a loan spell in the 2020/21 campaign, but according to David Moyes, there's no disappointment that Lingard now looks likely to ply to his trade in Saudi Arabia.
Asked about the move, Moyes said: "No disappointment at all (that Lingard is training with Al-Ettifaq).
"I'm quite comfortable and more than relaxed with it.
"We like Jesse a lot but I just don't know if we need another player in his position."