"It all depends what's on offer," Weir told BBC Radio Merseyside.
"Obviously it would be a great honour to come and work for Everton, I can't deny that. It's a massive club and it's got a big place in my heart."
The Scotland international, who has also had spells with Hearts and Falkirk, made 57 appearances for club and country this season.
His current deal at Rangers is due to expire in the summer but he has indicated his desire to play on.
"I've not ruled it out, so you never know," said Weir.
"I'll have a couple of weeks rest and then take it from there."
Source: BBC Sport
Source: BBC Sport