Chelsea have always been linked with a move to appoint legendary midfielder and all-time top goalscorer Lampard, although he has only just finished his first 12 months as a senior manager after his Derby County side were beaten by Aston Villa in the Championship play-off final last month.
It comes after reports Jose Mourinho could make a shock return to Chelsea for a third spell in charge - and after Rio Ferdinand described his former England team-mate Frank Lampard as "the flawless choice" for the Blues job.
Poyet has urged a former team-mate to seize the opportunity with both hands if he is offered the job, adding: "I think it's a lovely job and, if he has the chance, Frank has to jump at it".
"He is the flawless choice", he told the Mirror . He and [Derby assistant manager and former Chelsea youth coach] Jody [Morris] know all the kids from 16 upwards. That's true, but things aren't looking to get better anytime soon.
Benitez was appointed interim manager at Chelsea in November 2012 to replace Roberto di Matteo, just months after the Italian had won the Champions League. "I will actually be surprised if they look elsewhere".More news: Thailand - should you always celebrate scoring goals?
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"People talk about experience and what-not, but what experience did Pep have when he went into Barcelona's first team?"
The Spaniard's connection to Liverpool, and his rivalry with Chelsea and Jose Mourinho during his tenure at Anfield, made him a very unwanted man at Stamford Bridge.
Frank Lampard and Derby tasted defeat in the playoff final.
"So are you going to continue doing that, and keep blowing money away with these managers who you have to pay up after two years?"
"I doubt he'll go back to Chelsea.especially with the transfer embargo and the way the fans treat him last time".