Kosmina announced his resignation on Monday, claiming Adelaide United have 'no vision' and there is an environment at the A-League club that 'lacks trust'.

But at a hastily organised press conference, Griffin rejected Kosmina's claims, arguing Adelaide United had agreed in the past week to look into extending the 56-year-old's second stint with the Reds.

"On December 18, he went to a board meeting, he asked whether he could have an extension of his contract for two years at better money. We said that we'd look at it," Griffin said on Monday.

"We've got a board meeting on February 12. Between now and February 12 there would have been a series of discussions with him about what his expectations were, his salary terms, what our views were, how we saw the whole thing going forward.

"As far as we were concerned we had a process in place, which he agreed with and took no issue.

"To say that we are amazed by an alleged lack of trust is very, very significant."

Griffin added that assistant coach Michael Valkanis will take over the top job on an interim basis.

Kosmina took over as Adelaide's coach just over two years ago after Dutch manager Rini Coolen was controversially moved into a youth coaching role.

With Coolen having organised a payout with the Reds out of court last week, Kosmina's exit will hit Adelaide extra hard and, according to Griffin, they never saw it coming.

"I'm very surprised with the way the story has unfolded," Griffin said.  "I would have thought that if John had an issue he could have come and seen me or come and seen (CEO) Glen Elliott. 

"He's chosen to resign so we move on."

Adelaide dropped to fourth on the A-League ladder over the weekend as they lost 3-1 away to league-leading Central Coast Mariners on Friday before Melbourne Victory and Western Sydney Wanderers won on Saturday to move into second and third respectively.

Rumours emerged that Adelaide United were interested in replacing Kosmina with Valkanis, which prompted the South Australian club to send out a media release on Saturday completely denying the speculation.

Kosmina has quit his past three coaching jobs having also left the Reds following the side's 6-0 thrashing at the hands of Melbourne Victory in the 2007 A-League grand final, while he was replaced by Czech Viteslav Lavicka at Sydney FC in 2009 after poor results.