The former-Highbury striker identified the Danish boss as the man to step in should Wenger leave the Gunners at the end of the season.
The Arsenal manager has come under scrutiny after his side crashed out of the FA Cup to Blackburn, before slumping to a 3-1 home defeat to Bayern Munich in the Champions League last-16 first-leg.
These two defeats have all but ended Arsenal's hopes of ending their eight-year trophy drought for another season.
And Wright believes Laudrup would be an ideal candidate to take over at the Emirates Stadium should Wenger end his 16-year association with the north London club.
Wright told The Sun: "Laudrup could maybe step in, who knows? There is so much pressure mounting on Arsene now I would hate to see him go out like that.
"I have been shouting from the rooftops for many years now about the deficiencies in respect of replenishing the squad and buying the kind of player that is going to get Arsenal back to, not just qualifying for the Champions League, but getting past the quarter-final stages and really having a good go at it.
"If we are not careful we are going to end up going for fourth spot every single season and if that does not happen - then what?
"With Arsenal, apart from the Bruce Rioch situation, they aren't too quick to sack people.
"They've given Wenger time and put their faith in him. If I'm totally honest I think he deserves the time because of what he's done for the club and many people will agree.
"Personally I don't want to see Wenger go out on his sword, I want to see Arsenal get back to a situation where they are fighting it out with the big boys again."
Laudrup replaced Brendan Rodgers at the Liberty Stadium last summer, and the Dane has done a fantastic job in south Wales.
He leads his team out this Sunday for the Capital One Cup final against Bradford, hoping to win Swansea's first piece of silverware since they won the Football League Trophy in 2006.