Pearce has been looking for midfield craft since the £21m departure of Shaun Wright-Phillips and the 25-year-old French certainly fits the criteria.
City are expected to return to the Cottagers with an improved bid so that Malbranque can line-up for the Blues in Saturday's clash with Olympiakos in the Thomas Cook Trophy.
He could be joined in the midfield at the weekend by Joey Barton after the star impressed in a reserve game against Burton.
Barton has been receiving anger management lessons after his infamous clash with an Everton fan in Thailand saw him land a whopping fine.