But the 40-year-old says he will not decide on whether to continue playing until the end of the season.
Moyes told BBC Scotland that he would love Weir to join his backroom staff.
"Why wouldn't you be interested in something like that? It's something that a lot of people would cut their right arm off for," responded Weir.
"I go into Everton regularly. I am still based in this area and still got a lot of friends there and have a lot of ties there and I've got a great relationship with the manager there."
Weir, who played under Moyes at Goodison before his switch to Rangers in 2007, is out of contract in the summer but could be offered a new deal, especially with the Ibrox club's ability to sign new players being restricted by their bankers.
"Like I have said for the last few years, I will just wait until the end of the season and make a decision then," Weir told BBC Scotland.
"I am enjoying what I am doing just now and take it day by day."
Weir had come in for some criticism after recent defeats by Celtic in the Scottish Cup and Scottish Premier League.
However, he lifted the Co-operative Insurance Cup on Sunday having turned in an assured display throughout a gruelling 120 minutes as Rangers beat their Old Firm rivals 2-1 after extra time.
"You don't enjoy when people write you off and there are plenty of people who have written me off and plenty of people who have written other players in the team off, but that goes with the territory," said Weir.
"You can throw your toys out the pram or you can go and try to answer them in the right manner and I think the team have done that."
Moyes named Weir his man of the match while working as a pundit during BBC One Scotland's live television coverage of the Hampden final.
"I would love to have him back at Everton as part of my staff in the future, if he's interested," said the Everton boss.
"He's a great professional and someone who all the players at Everton and Rangers should look up to.
"I thought last year he would probably call it a day. He may only have 10 or 12 weeks to go as a player.
"But, on that performance, he's doing great and I think Davie will know best when the time comes."