Kennedy: Paul Marsden has friends among Lib Dems
Speaking on the BBC's Breakfast With Frost programme, Mr Kennedy said he was not put off by reports that the defiant MP was "a handful".
Mr Marsden has accused backbench colleagues of acting like "thugs" after he spoke out against the war in Afghanistan and the anti-terror measures.
He is due to face a meeting with the party's chief whip to explain his allegations.
Rumours have circulated that the Shrewsbury and Atcham MP is considering a move to the Liberal Democrats.
Mr Kennedy said: "I would welcome anyone with open arms who subscribes to the values, philosophies and principles of the Liberal Democrats.
'Thugs'
"It has to be a decision for Paul Marsden himself to take. He has made pretty clear in his own words, rather graphically over the last while, his unhappiness with the state of the Labour Party."
In a two-page article in the Mail On Sunday, Mr Marsden outlines his campaign against what he calls "Labour thugs" who he claims have bullied him over his anti-government views.
He claimed fellow MPs verbally and physically "attacked" him during a debate, an allegation they deny.
Mr Kennedy said Mr Marsden's reputation did not concern him.
"When you're leader of the Liberal Democrats a bit of a handful goes with the in tray," he David Frost on Sunday.
He said of Mr Marsden: "He has Liberal Democrat MPs who are neighbouring MPs and they are pals and personal friends.
Meeting
"He has talked on personal terms among my colleagues but then again he has probably talked to Conservatives as well."
He stressed that any decision to defect would have to come from Mr Marsden.
But the Liberal Democrat leader's views differ to those expressed by colleague Simon Hughes, the party's spokesman on home affairs.
Talking on GMTV's The Sunday Programme, he said he would advise Mr Marsden not to join the Liberal Democrats, but to become an independent instead.
Mr Marsden is due to meet government chief whip, Hilary Armstrong on Monday, to explain comments he made about fellow Labour MPs.
She is also due to question him about a press release wrote detailing his alleged intimidation by colleagues.
Mr Marsden has described his party as having a "dangerous New Labour clique" stamping out dissent.