The VW Group-owned car brand has contacted agencies with a view to running pitches with prospective agencies in May.
As well as creating above-the-line advertising, Skoda is looking for a global agency to provide CRM, digital and social media comms solutions.
Fallon was given Skoda’s European advertising account in 2014, having held the UK business since 1999. The Publicis Groupe agency then opened a Prague office which has around 50 employees and, according to its website, is "working mainly on the global Skoda account".
Skoda wants to have a new agency in place by September, if it decides not to reappoint Fallon, for a minimum three-year period which could be extended to five years.
However, Skoda has told agencies that the global agency would be expected to continue working with local agencies, indicating that Fallon would continue to be the brand’s UK ad agency.
PHD handles VW Group’s media planning and buying after winning the global account in 2016.
Last year Skoda announced Olympic cycling champion Sir Bradley Wiggins as its brand spokesman in a three-year deal.
The brand then launched "The ride", the first ad featuring Wiggins, which kicked off Skoda's "Driven by something different" positioning which aimed to establish the marque as a premium brand.
Skoda did not respond to a request for comment.