However, if JWT does not supply the winning idea, sources say it will still be asked to implement the campaign.
JWT has held the telephone and internet banking account since January 2005.
However, First Direct still uses branding work developed by its previous agency WCRS.
The pitch comes after the departure of Peter Simpson, First Direct's commercial director, last week.
Sources close to the account said WCRS's work for it was popular with Simpson.
An HSBC spokesman said: "We regularly look at all our agencies. It's not a pitch or a repitch, it's just normal work with our agencies."
The JWT global client leader and chief executive Toby Hoare denied there were any changes in JWT's relationship with First Direct.
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