The two parties are understood to have held informal talks about the possibility of the two companies working together more closely.
The talks are thought to have covered a range of options from a partnership to a merger.
The companies have confirmed that they are in talks, but deny any plans for an outright merger at this stage.
A spokesperson for Freud, said: "We categorically deny plans to merge but confirm we have held talks to discuss ways that our two companies could work more closely together."
It is thought the companies could compliment each other because Chime's core business is corporate PR, through Bell Pottinger, and it wants to expand it consumer PR division. Chime also owns the advertising agencies HHCL & Partners and Roose.
Freud does more consumer work and represents celebrities such as Geri Halliwell and Chris Evans. It has recently been beefing up its corporate division, winning clients such as Nike, Nestle and Unilever.
Reports of the merger follows a more than £100m drop in Chime's market value in the last few months.
It could be second time lucky for Freud. Only last year the directors of Freud completed a £10m management buy-out of the firm from the AMV Group.
The AMV Group, which owns ad agency Abbott Mead Vickers, bought Freud from founder Matthew
in 1994.
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