The news follows a leaked opinion poll that he commissioned and which, it's been claimed, undermined party leader Nick Clegg.
Oakeshott's said the party's "heading for disaster" under the leader.
The row's been escalating after the existence of the poll emerged, following the European elections, in which the Lib Dems didn't fare very well.
Clegg's faced having his leadership called into question by a number of constituency associations, with activists urging him to step down.
Business secretary Vince Cable, a long-time confidant of Oakeshott, has condemned the poll.