Swedish coach urges Celtic to take Rafa Benitez away from Newcastle United
Newcastle fans are desparate for Benitez to stay at St James's Park with his contract set to expire in the summer.
However, the Spaniard's future remains unclear after he revealed last week he is "waiting for an answer" after holding talks with the club's hierarchy.
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Hide AdBenitez, up until now, has just five games left as Magpies boss - and Mjallby believes the SPL giants should take full advantage of the situation.
The former defender wants the Hoops target well known bosses such as Andre-Villas Boas, Roberto Martinez and Benitez.
“Why not?” said Mjallby. “You can’t talk Celtic down.
“Obviously, Rangers have had difficult years but they are massive clubs and either one of them should win the league every year.
“But even if you have been the manager of big clubs in other major leagues, the pressure you have as a Celtic manager is enormous.
“Martinez has never won a league title, for example.
“Villas-Boas and Benitez have done, but you have the chance to win trophies every year at Parkhead.
“The ambition should also be to make Celtic great in Europe again.”