In a statement, Nader, a Sirius shareholder, said Liberty Media Chairman John Malone's $3.68-a-share offer was below the $4 where the company was trading a few weeks ago. Nader callied the bid "ludicrous." Liberty currently has a 52-percent stake in Sirius, but would take full ownership in the potential deal.
"Carl Icahn—take notice and interest," Nader said in his statement.
Icahn has not responded to Nader's comments. Last week, Icahn purchased 30 million to 40 million shares of car rental business Hertz, according to sources.
(Read more: Icahn takes stake in Hertz: Sources)
This isn't the first time Nader has reached out to Icahn. In December, he asked corporate reformers and shareholder activists—including Icahn—to pledge 1 percent of their net worth annually for three years to help start a corporate watchdog movement.
Shares of Sirius jumped nearly 7 percent Monday. Liberty Media shares were lower. Still, Wunderlich Securities upgraded the company's shares to "buy" and maintained its $170 price target, a level the stock pulled back from in the last month. The brokerage also called Liberty's offer "favorable" to SiriusXM shareholders "under nearly all plausible operating scenarios for customer growth and pricing."
Malone has a long history of media acquisitions. Last May, Liberty Media completed a deal to acquire a 27-percent stake in Charter Communications.
Read the full statement from Ralph Nader here:
"John Malone's offer to buy out Sirius XM's shareholders at $3.68 a share is ludicrous. Sirius XM was trading over $4.00 a share just a few weeks ago and is a fast growing company with bright indicators and registers four stars by Standard & Poor's which recommends a buy. I am sure that I along with other shareholders in Sirius XM will be interested in a legal challenge to John Malone's company for low-balling Sirius XM's shareholder value. Carl Icahn—take notice and interest."
—By CNBC's JeeYeon Park. Follow her on Twitter @JeeYeonParkCNBC.