The Swede will step down as Lennon's assistant manager after the SPFL Premiership champions bring down the curtain on another successful season, with tomorrow's clash with St Johnstone and Sunday's title party at home to Dundee United the final two fixtures of the campaign.
Former Hoops defender Mjallby has been Lennon's faithful lieutenant since he succeeded Tony Mowbray four years ago and the Parkhead boss will continue to take his time before appointing his new sidekick.
Lennon said: "To be honest, I haven't really sat down with Peter Lawwell yet and discussed it. There is not any rush on it.
"It doesn't have to happen by the end of the season but hopefully coming into pre-season and the start of it we will have someone in place.
"It is a blow to lose Johan, he is my right-hand man and has been from day one.
"It will certainly be different not having him here and while I am disappointed to lose him I can understand his reasons for it.
"It is not important [to have an affinity with the club]. It will be someone who can bring something fresh to the backroom team.
"If he does have an affiliation with the club then even better."