Liverpool boss Brendan Rodgers says Raheem Sterling "is being led by his representative" as he seeks a move.
Aston Villa manager Tim Sherwood has revealed in-demand defender Ron Vlaar has told him he wants to stay at the club.
Interim manager Benitez claimed the Stamford Bridge decision-makers who have halted contract talks with the England midfielder had no doubt about "his condition, his levels, his quality".
Benitez suggested owner Roman Abramovich and the board were analysing "different things", but did not go into more detail.
It is only possible to speculate what they might be but one could be the fact that Lampard is one of the highest earners at the club during an era of Financial Fair Play.
His age, 34, and recent injury record might also come into it but Benitez told BBC Sport: "For sure, he's a fantastic player, a great professional - there's no doubt about this.
"Also, when I talk to the people in charge, they are telling me the same, so nobody has any doubt about his condition, his levels, his quality.
"So the decision could be analysing different things, not just the quality of the player."
Lampard insisted he had "two or three years at least" left to give as an elite footballer - even if Chelsea appeared to think otherwise.
He admitted on Thursday his glittering career with the European champions could be drawing to a close after revealing he was not in talks with them over a new contract to replace the one that expires next summer.
Lampard appeared resigned to his fate after helping Chelsea into the Club World Cup final in Yokohama, coming off the bench against Monterrey for his second appearance since recovering from a troublesome calf problem.
That compounded an injury-hit 2012 but Lampard made it clear he had more to give.
"I feel like I have two or three years, at least, in me at the top level," he said.
"It is not for me to decide on this one. It's up to the club.
"Whatever happens, I have had a great time at Chelsea. I am determined to play a few more years and see what pans out in the near future."
Lampard, whose 11 years' service at Chelsea and third place in the club's all-time list of scorers has seen him become an heroic figure there, added: "There have been no talks about anything about an extension.
"Maybe things don't last forever. Although I want it to last forever, you have to be big enough to know what it is."
Lampard has been linked with moves to Los Angeles Galaxy, Chinese club Guizhou Renhe and a host of other clubs - even Chelsea's Barclays Premier League rivals Arsenal.
Already short in midfield, Chelsea are unlikely to let him leave in January but he could sign a pre-contract agreement elsewhere.
Lampard added: "I'm not the kind of player to see out my time and sit with my bum on the bench too much. I want to be involved.
"I will keep trying to do that, whatever the circumstances."