The QPR manager believes the Stamford Bridge side should do everything they can to prevent the England duo leaving for free when their contracts run out in the summer of 2013
The contracts of both expire at the end of the season, and with no new deals announced as of yet, they will be free to talk to foreign clubs in January about a free move in the summer.
But the new coach of the Hoops thinks the England duo are the "backbone" of the Stamford Bridge side, and can remain an integral part of the squad for years to come.
"For me, it would be total madness to get rid of the likes of Frank Lampard, who is 34, and Cole, 32," he wrote in The Sun.
"Age is just a number as far as I am concerned - and I don't mean a number on a bank balance sheet.
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"While I can understand why some clubs pursue a policy of getting 'older' players off their books, it must never happen at the expense of hurting the team.
"Whatever superstars Chelsea have, and they have many - [Juan] Mata, [Eden] Hazard and Ramires to name three - Lampard, [John] Terry and Cole remain the backbone of the Chelsea team."
Redknapp suggests managers should look to the example of Milan legend Paolo Maldini when considering the impact older players can still have for clubs.
He continued: "Paolo Maldini was around 42 when he retired after playing at a world-class level for his entire career spanning two and a half decades.
"It beggars belief that 'Il Capitano' might have been put out to grass just because he turned 30 along with Franco Baresi, his defensive partner for club and country."
And the 65-year-old feels clubs such as Arsenal with exciting emerging talent would do well to trust in the experience of older players in order to steer them through difficult games.
"A terrific, talented, young side is emerging at Arsenal but maybe with the inconsistency they have shown this season, it could be because they do not have the blend of experience needed in the dressing room," he added
"Older players do not have to be offered long-term contracts like Arsenal have given to Jack Wilshere, Alex Oxlade-Chamberlain Aaron Ramsey, Kieran Gibbs and Carl Jenkinson.
"But without the right experience, they could end up coming unstuck."