The proposal comes after Icahn reported Friday a 12.12 percent stake in the auto services and retail company. Pep Boys previously reached a deal in October to be acquired by Bridgestone for $15 per share, or $835 million.
"We believe our proposal is clearly superior to the $15.00 per share Bridgestone transaction and that our financial wherewithal to close expeditiously is indisputable," Icahn Enterprises wrote in a letter to Pep Boys.
Pep Boys shares closed Monday about 2.4 percent higher.
The Icahn letter said that the proposal would not be subject to "any due diligence, financing or antitrust conditions."
Earlier Monday, Pep Boys noted that Icahn Enterprises previously offered $13.50 per share for the company at an undisclosed date. In late October, Icahn said it would not increase the value of the proposal.
In a Securities and Exchange Commission filing last week, Icahn said Pep Boys' auto parts segment "presents an excellent synergistic acquisition opportunity" for Auto Plus, which is owned by Icahn Enterprises. The billionaire investor's representatives have held talks with Pep Boys and "various parties" about possible transactions involving its retail arm.
Pep Boys did not immediately respond to a request to comment.