The search for the new Parkhead boss is well under way after Northern Irishman Lennon stepped down on Thursday having led the club to three Scottish Premiership titles during his four-year spell in charge.
Lennon's former team mate Larsson immediately became one of the front runners for the post in a field of constantly-changing favourites which includes names such as Owen Coyle, David Moyes, Malky Mackay, Jackie McNamara, Roy Keane, Steve Clarke and Paul Lambert.
Nilsson said that an unnamed club had intimated their interest in the former Sweden striker but was "not worried" about losing his boss.
He said: "I spoke to Henrik today as I speak to him every day and he told me he was staying.
"He told me a club wants to speak to him but he will stay with Falkenbergs this season and in Sweden the season lasts until November.
"I know Henrik as a man and when he says something he stands by his word so I am not worried about it.
"We have a game on Saturday and we are just focused on that."
Lennon will assist Celtic chief executive Peter Lawwell in choosing his replacement and he backed Larsson to be successful if he was to be his replacement.
Speaking to STV and Sky Sports at Glasgow airport before jetting out to Lisbon for the Champions League final with the Lisbon Lions, the players who won the European Cup for Celtic in the city in 1967, Lennon was asked if the former Hoops' hit-man was ready to step into his shoes.
He said: "You will need to ask Henrik that but if he does I am sure he will be a huge success. Why not?
"He's had a fabulous career as a player, he is a very intelligent guy and knows the game very well."
Lennon told Celtic's majority shareholder Dermot Desmond of his decision earlier in the week, insisting that the conversation was "very amicable, very open, as it always is."
He said: "I have had a great relationship with him and again I am eternally grateful for the opportunity, the advice and the learning curve that I have had working under him, and with a very strong board as well.
"The board did everything for me. They gave me the opportunity when a lot of people thought I wasn't ready for it and four years down the line we have had a lot of success which is something we are very proud of."
While many people thought Lennon was set to walk straight into a job in England upon his departure, the former Celtic skipper claimed that there is nothing immediate in the pipeline although he admits working down south is an ambition
"It's a decision I have come to and it might not be in the short term, it might be a long-term thing ," he said.
"It's an ambition (to work in England) but I need some time to digest it all. Leaving Celtic is a huge wrench.
"I will probably never leave it in my mind but physically I will do.
"I have been associated with the club for 13 years and I am sure I will still have an association with it.
"I just need time to think things over. I won't rush anything. I don't know if opportunities will come up.
"People say it is a bit of a gamble but I just felt that the time was right for me and my staff to take our careers in a different direction.
"I left the club in a great position, from when I took over.
"On and off the field we are very strong and our reputation in Europe is very good."
Lawwell insists Celtic have not yet approached anyone and will exercise due diligence in the process.
He said: "It is very early to make any comment, I am sure you will understand. It is very early in the process.
"We will take as much time as it needs to get the right candidate and we have got a wee bit of time so hopefully we will get it right."