Pitches for the account, which is held by Faulds Advertising's sister media division Media Faulds, are being held over the next few weeks.
The media review follows news that the automotive chain had entered into talks about its creative account.
Faulds has held Kwik-Fit's account since 1999, when it won media from CIA Medianetwork Scotland and creative from the Morgan Partnership.
It was acquired by the venture capitalist CVC Capital Partners from Ford for £330 million last July. Ford had bought Kwik-Fit in 1999 from its founder, Sir Tom Farmer. Following its sale, Ford admitted it had taken a $1 billion hit on the business.
CVC also owns Halfords, which it acquired from Boots last year. After the purchase, CVC shifted media out of MindShare, Boots' agency of record, into OMD UK.
City analysts have suggested that Kwik-Fit and Halfords could be a good merger.