In Germany, the parties in the ruling coalition select cabinet ministers. Seehofer's refusal to allow Glos to exit the government leaves the ruling coalition in political limbo with seven months to go before a general election.
Glos offered to quit earlier Saturday in a letter to Seehofer, a spokesman for the economy ministry told AFP.
In the letter, leaked to daily Bild, 64-year-old Glos said he wanted to resign due to his advancing age and a drive by Seehofer to change the face of the CSU after a disastrous state election in September.
"Renewal, the ability to set the agenda and credibility are needed now more than ever," Glos said of the party.
But the CSU spokesman said Seehofer had assured the minister of his confidence in him and asked him to stay.
"I will discuss the reasons for his decision cited in his letter in a personal conversation with him," Seehofer said, according to his spokesman.
With elections approaching, the party has struggled to get its house in order after being humiliated in a Bavarian state poll in September last year.
Merkel is running for re-election in September 2009, and although her personal popularity rating remains high, the same cannot be said of the CSU, whose votes she needs to win.
The conservatives are hoping to garner enough votes to jettison their current "grand coalition" partners, the centre-left Social Democrats (SPD), and govern with a more ideologically similar party.
Since the economic crisis began, Glos has been largely sidelined, perhaps due to differences with Merkel. Finance Minister Peer Steinbrück - from the SPD - has generated far more headlines.
He repeatedly challenged the chancellor to cut taxes even after she had categorically rejected the proposal.
But when Merkel did an about-face last month, unveiling a €50-billion ($66-billion) stimulus package full of tax relief, he was kept far from the television cameras.
Glos was an influential figure in the conservatives under former Chancellor Helmut Kohl. He became economy minister in 2005 when CSU chief and failed chancellor candidate Edmund Stoiber turned it down.
"My work as minister for the economy and technology has been the high-point of my political life," he wrote in the letter published by Bild. "First and foremost it was important to me to implement quickly effective measures in the financial and economic crisis that also carried my signature," he said.
Bild said Glos had informed Merkel that he was quitting while she was in Munich for an international security conference. The ministry spokesman said he was unable to confirm this.