Grender is running the party's PR department until February, when it hopes to appoint Norman's successor.
Grender was involved in recommending the creation of the role a year ago to ensure key messages were consistent with policy pronouncements.
She said the Lib Dems wanted a comms figurehead to ‘take us through to the next general election'.
Sources close to the party have suggested former WWF lobbyist Norman was ousted after only eight months in the role - a charge the party denies. Grender ran the Lib Dems' press office from 1990-95 and the overnight operation for the 2001 election.