However, a Parkhead source later said the claims were "complete garbage", while Jansen has recently denied interest in a return to Celtic.
The claims came after Roberto Martinez was quoted expressing interest in moving to Parkhead, although Celtic are increasingly likely to face serious competition from Wigan if they continue to pursue the Swansea manager.
Martinez is expected to discuss Celtic's approach with his employers when he returns from holiday on Wednesday.
Celtic's initial request to interview Martinez was rebuffed but Swans chairman Huw Jenkins has admitted he will not stand in the Spaniard's way if he insists on meeting Parkhead chief executive Peter Lawwell.
The 35-year-old appears destined to do so after apparently saying "any young, aspiring manager with ambition would be interested in a job like that".
But Wigan's impending managerial hunt could scupper any hopes Celtic maintain of luring the former Motherwell midfielder, who led Swansea to the League One title in his first full season and then eighth place in the Championship this season.
Wigan manager Steve Bruce is negotiating personal terms with Sunderland and the compensation package from that deal would cover the four years remaining on Martinez's Swansea contract.
Wigan chairman Dave Whelan has already admitted Martinez, a celebrated former Latics player, would be at the forefront of his thoughts when he begins moves to replace Bruce.
Whelan told the Sun: "Roberto would be near the top of any list we formulate."
Meanwhile, Adams claimed he was in the frame to succeed Gordon Strachan if Jansen made a sensational return to the club he led to a famous title win in 1998.
Adams told talkSPORT: "My good friend Wim Jansen is probably in at Celtic. It would be him as technical director and me as manager."
The former Arsenal skipper added: "I've not applied for the role. I know Wim Jansen, who has put me in there.
"I think they approached him, and I know Wim from my Feyenoord days, and he's actually said that he would only do the role if I were to be made manager. That's Wim's opinion, not Celtic's."
Adams, who worked under Jansen during a six-month spell as Feyenoord under-21 coach in 2005, added: "By saying manager, it is kind of a head coach's position really because once you have a technical director like you have in Europe, they help you with recruitment.
"As long as you have the final say of who comes in and out, these people are your help in the boardroom.
"I never had that at Portsmouth. It works for me and Celtic is an unbelievable club - you have a 50% chance of winning something up there."
Although Jansen left Celtic after one season, following a disagreement with then general manager Jock Brown, he remains a hero after stopping Rangers claiming a 10th title in a row, one more than Jock Stein achieved at Celtic.
The former Holland international also won the League Cup and brought Henrik Larsson to Parkhead - the £650,000 fee securing a return of 242 goals.
But Jansen, who stepped down from his role as Feyenoord assistant in January, has recently denied interest in a return to Glasgow.
He told the Sunday Herald: "I want to do something in football. but I am not interested in the Celtic job, whether as an assistant or head coach."
Martinez remains a far more likely candidate but several names continue to be mentioned in relation to the role.
West Brom have repeatedly warned Celtic off making an official approach for Tony Mowbray while Motherwell manager Mark McGhee and Dundee United boss Craig Levein have consistently been linked.
Owen Coyle was thought to be Celtic's first choice but he pledged his commitment to Burnley before going on holiday at the weekend, although he is yet to sign a contract extension.