Claiming his position "is a gift of 13 senators," Drilon said he would gladly turn over the post to "anybody who can muster enough votes" to replace him.
Drilon refrained from giving further comment out of respect to Roxas who also belongs to the Liberal Party.
Drilon led some members of the Liberal Party that included Senate Majority Leader Francis Pangilinan in joining the opposition-led call for Mrs. Arroyos resignation last July 8.
However Roxas, also a Liberal kept his distance from his party mates stance.
Drilon was scheduled to meet with Liberal Party leaders at Roxas residence as part of the regular Tuesday meeting of the party to discuss various issues.
He stressed the issue of who would become the next Senate president was not a topic of discussion.
Administration Sen. Miriam Defensor-Santiago last Monday welcomed reports that Roxas was included among the senators said to be eyeing Drilons seat.
Santiago said a "wider menu of options" is better for Malacañang insofar as the number of administration senators looking to head the Senate.
Roxas, for his part, has refused to answer questions on the unconfirmed plan by the Palace to support him as a possible replacement for Drilon.
Sen. Lito Lapid was also quoted in radio reports as saying that Mrs. Arroyos political adviser on legislative affairs Gabriel Claudio had mentioned Roxas as Drilons possible replacement.
Drilon has since said he is not keen on keeping his post and would rather give it up to any contender who can muster the needed 13 votes.
Sen. Sergio Osmeña III had earlier described Drilon as "a Senate president only in sufferance," meaning he was merely tolerated by his colleagues.
Santiago was said to be aspiring for the Senate presidency, but for her part, she noted she would have to gain the support of both the administration and the opposition.
However, Sen. Manuel Villar, chairman of the Senates committee on public order and illegal drugs, as well as the committee on finance, pointed out an existing term-sharing agreement with Drilon, which is set to turn over to Villar in January.
Villar was seeking the Senate presidency after the last election but gave way to Drilon with the term-sharing arrangement.
If Malacañang endorses Roxas, this could minimize Villars chances of taking over the Senate presidency.
Although Villar was recently lauded by Mrs. Arroyo for pushing the passage of the anti-terror bill, the President is unlikely to forget that Villars wife, Las Piñas Rep. Cynthia Villar, was among the administration lawmakers who supported the opposition-initiated impeachment complaint against Mrs. Arroyo.