The agency's chances have been boosted after the decision of Richard Baker, Boots' recently appointed chief executive, to part company with Francke. Baker is a former marketing director of Publicis' Asda client.
Final presentations from the four shortlisted creative agencies - the incumbent, J.Walter Thompson, Abbott Mead Vickers BBDO, Publicis and Mother - will be completed over the coming weeks.
An announcement on who has won the business, worth an estimated £44 million above the line, is expected on 20 November.
Francke, who leaves Boots after less than ten months, has not been replaced.
David Kneale, the operating chief, becomes the chief commercial officer as part of the shake-up to "simplify and focus the leadership", according to Boots.
Francke said: "It was made clear to me by Richard that the decision about creating a new smaller executive team was not about performance or personality."
She added: "I think there has been real recognition of the change that I brought about in the time I was there, but I'm philosophical about these structural changes."