Reports in Italy have claimed that the Florence outfit have joined the chase for Lampard - who is free to talk to foreign clubs with his Chelsea deal due to expire in the summer.
The likes of Los Angeles Galaxy, Monaco and Juventus have all been linked with Lampard in recent weeks, whilst clubs from across Asia are also said to be keen on securing his signature.
But now Fiorentina could be ready to offer him a deal to move to Tuscany in the summer.
"Lampard is a player I have always liked and may be an example of today's marketplace," Cognigni told La Gazzetta dello Sport.
"A player who has passed 30 years, his contract is expiring, and he may be the right combination between experience and cost of the deal."
However, Cognigni admitted that transfer plans were not his department and it was not his decision.
"Market choices are not up to the chairman but to our market men Daniele Prade [sporting director] and Eduardo Macia [technical director]".
Lampard was backed to make the move by current Fiorentina star and former West Bromwich Albion midfielder Borja Valero.
"Lampard to Fiorentina? Players of that level would be perfect for Fiorentina and it is beautiful if they arrive. But the market is dealt by our officials, I just think about playing," he said.