Wyllie confirmed she was in talks with several agencies about the account, which Lansons Communications has held for five years.
Lansons is defending its Jupiter work against several suitors including Penrose Financial, Mainland and Quill Communications. Wyllie would not comment on fees for the account.
In addition to strategic advice, a significant part of Lansons' role has been to act as Jupiter's press office.
Wyllie said her appointment and the establishment of an in-house PR team were the main reasons for the pitch, though she said it would not necessarily mean that fees on the account would be cut.
'We're very open minded about what we're going to spend. It's much more about getting value for money and making sure that our comms support doesn't overlap,' Wyllie told PRWeek.
Wyllie's appointment as Jupiter's first head of retail comms last September marked an upwards shift in gear for Jupiter, whose press office Lansons has supported.
Wyllie worked as a freelance journalist before joining Jupiter last year, but was assistant editor of The Sunday Times's Money magazine until 1999, and then managing editor of UKinvest.com, Freeserve's personal finance website.
Her main responsibility has been to raise Jupiter's profile in the business press. On Wyllie's appointment last year, Jupiter Unit Trust Managers MD Gordon Davidson said he expected her to position Jupiter more as a commentator on investment.
With this in mind, the fund manager has sought to push forward prominent fund managers, such as joint CEO Edward Bonham Carter, who frequently offer their views on investment climate to the national press.