Cole, England's greatest ever left-back, is set to move to the promotion chasing Rams 'in the next 48 hours'.
The Daily Mail report that the 38-year-old has agreed terms on a six-month, £15,000-a-week deal at Pride Park.
England centurion Cole has been out of contract since leaving MLS side Los Angeles Galaxy in October last year.
Derby owner Mel Morris was reportedly convinced by Lampard to sign the veteran to provide cover should injury strike.
Cole, who has kept himself in shape, is said to be still unsure on when to call it quits on a stunning, trophy-laden career.
With Arsenal and Chelsea, Cole won the Premier League three times, a record seven FA Cups, the League Cup, the Europa League and the Champions League.
He also won 107 England caps and was regarded as the best in his position in the world while in his prime.
Lampard, who won the Double in 2010 and the Champions League alongside Cole in 2012, previously said: "He would bring quality and experience.
"I speak to Ash all the time. He's a great lad and I know he's fit, fresh and wanting to continue to play.
Ashley Cole honours
Honours
- Premier League titles: 2001-02, 2003-04, 2009-10
- FA Cup: 2001-02, 2002-03, 2004-05, 2006-07, 2008-09, 2009-10, 2011-12
- League Cup: 2006-07
- Champions League 2011-12
- Europa League: 2012-13
Individual awards
- Record seven FA Cup winners' medals
- 107 England caps
- PFA Team of the Year: 2003, 2004, 2005, 2011
- Uefa Team of the Year: 2004, 2010
- Euro 2004 Team of the Tournament
- Chelsea Players' Player of the Year: 2009, 2011
"I know the influence he would have but it has to be right for all parties.
"In my opinion, he's the greatest left-back of a generation.
"Of course, his age is an obvious thing but it's not a problem for me.
"I think it's pretty clear that we're interested in Ashley."
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