Wenger will leave Arsenal at the end of the season after almost 22 years at the club.
Enrique is the favourite with the bookies to take on the job at the Emirates.
The Spaniard has been out of management since leaving Barcelona at the end of last season.
Smith says Enrique would be perfect for Arsenal but says his high wage demands may be an issue.
“They’re not too far away from the top four I don’t think,” Smith said of Arsenal on Sky Sports.
“They’re a long way away from fighting for the title as their points deficit over the last 10 years has shown between them and the winners.
“But there’s so much potential here.
“These managers will be scrambling over hot coals I think to get this job as long as the money’s right.
“For me Luis Enrique would be the perfect fit.
“The word is he wants an awful lot of money, maybe more than Arsenal want to give.
“But I think the style of football that he plays, the fact he’s available, he’s got a great track record, it’s something that would excite these fans.”
Arsene Wenger’s final few weeks at Arsenal started with a 4-1 win over West Ham today.
Source : EXPRESS