The Hoops assistant boss has decided to call time on his four-year stint as Lennon's number two and instead seek a fresh challenge away from Parkhead.
But the former Celtic defender does not think the Northern Irishman is ready to head for England just yet.
Lennon has been linked with the manager's position at Norwich and Mjallby is confident his friend can make a success of himself south of the border one day - but only after he finishes his job with the three-in-a-row champions.
Mjallby said: "Neil is under contract and I don't see any reason why he would leave. He hasn't told me anything about that so if you ask me I think he will still be here.
"He has improved tactically since we first got together and he has calmed down a bit too, which will stand him in good stead. I think he will go on to have a very successful career as a manager."
But the former Sweden international insisted ex-Leicester midfielder Lennon will not be able to ignore his ambitions to work in the Barclays Premier League forever.
"He's hungry to improve and I can see him moving to England at some stage - definitely at some stage," he warned.
"Why not? He knows the British game and has played down south, so obviously I can see him moving there one day."
Mjallby joined Celtic as a player from AIK Stockholm in 1998 and won three Scottish titles under Martin O'Neill as well as helping the Hoops to the UEFA Cup final in 2003.
His spell as a Parkhead coach was just as successful as he played a part in another three league triumphs on top of last year's run to the Champions League last 16.
"I feel quite brave leaving such a massive, successful club but it's time to do something else," said Mjallby ahead of Saturday's Scottish Premiership clash with Aberdeen.
"That is my only reason for leaving.
"I have been thinking about it for quite a while and now it is official. I just feel I'd like to work for another club.
"We have put Celtic on the European map. Financially we are not as strong as when I was here as a player so there is a feeling that I have achieved everything I can here. We have won the title three times running so maybe it is time for the club and me to part ways.
"Would I like to be a manager in my own right? Yes, in the future. I'm still happy to be an assistant but I'm confident I could do both roles."
But Mjallby shot down suggestions he was heading back to his homeland after lining up a job in advance.
He said: "There have been a lot of rumours that I will only work in Sweden but that is not the case. I'm open to any offers. But I'm not weighing any up now, definitely not."
Meanwhile, the departing coach said Celtic will look into striker Anthony Stokes' recent visit to a Belfast bar to decide if he breached club rules.
He added: "We always deal with situations like this. It will be up to the manager and the club to sort that out.
"(Anthony) has been great for us this season and he is a very talented boy, a very good footballer. But obviously now and then he doesn't behave as well off the pitch as he does on it.
"Of course it is disappointing when small things like this happen but we need to look into it and hopefully make the right decision for the club and Stokes.
"We can't look after him 24/7. First and foremost, the most important thing is that (the players) do the right thing on the pitch for the club but it is also important that they behave off the pitch as well and show they are great ambassadors for youngsters, so it is disappointing in that respect."
Meanwhile, Celtic could be without Greek striker Georgios Samaras for Saturday's Scottish Premiership match against Aberdeen after he was stuck low by illness.
Right-back Mikael Lustig, however, hopes to step up his recovery from a recent hip operation by starting his first match in more than four months after he was given a 20-minute run out in the 6-0 thrashing of Inverness last week.
Midfielder Nir Biton and wide man James Forrest remain out with groin injuries, along with winger Derk Boerrigter, who has an abdominal problem.
Provisional squad: Forster, Matthews, Van Dijk, Mulgrew, Lustig, Ambrose, Izaguirre, Brown, Griffiths, Kayal, Commons, Pukki, Balde, Samaras, Stokes, Johansen, Henderson, Fridjonsson, O'Connell, Zaluska, Herron.