Consolidated Communications is among the shortlisted agencies, which is also believed to include MacLaurin, The Red Consultancy, Countrywide Porter Novelli and Hill & Knowlton.
The pitches will be presented to the cable operator later this week.
The campaign will focus on Telewest's consumer broadband cable service, aiming to showcase Telewest as the UK consumer's broadband champion. Additional elements of the campaign will include Telewest's digital TV and telephony services.
Telewest recently joined forces with its UK counterpart NTL to launch a joint marketing campaign to promote both operators' broadband cable services.
The companies are understood to have committed under £10m to the joint initiative, which aims to speed up the take-up of high-speed, always-on internet access to consumers for £24.99 a month.