Diaby, 29, was released by the Gunners when his contract expired during the summer having been hit by a number of serious injuries over the last four years.
The France international managed just two appearances over the previous two seasons but has been offered a Premier League lifeline by the Baggies – with head coach Tony Pulis confirming an offer is on the table and that he hopes to get Diaby back to playing regularly.
“Diaby came in, he had his medical yesterday. We’ve made him an offer and we shall see,” Pulis said after West Brom’s 4-1 pre-season win at Swindon on Saturday.
“The big thing with Abou is getting him fit and having the confidence from the medical team to do that. He is a top player and I mean he is a top, top player.
“We’ve had a look and we think there are things he can do to improve his chances of playing 30 Premier League games and we’re confident we can help him do that. Whether he accepts that and the ethos of the football club we’ll wait and see.”
Meanwhile, his former manager Wenger wished Diaby well and said the player deserves another chance at making an impression during the remainder of his playing days.
“I think Diaby is the biggest regret of my career,” the Arsenal manager said.
“He is a guy who has been severely injured and it is not acceptable, we have paid the price for that but I hope things turn around for him and they go well.
“First and foremost, he really didn’t achieve his potential unfortunately. I think he had great potential and he could only show that at certain periods of time.
“I’m a really big fan of Abou Diaby and I really hope from the bottom of my heart that he can end his career without any more injury concerns.
“It is a good experience for him, it is good for him to have a fresh start. He is 29 and can have three or four years at the top level.
“The fact that there was so much competition here makes it so much more difficult for a player who has been out for such a long time.”