The offer has come from Hallwood, which had previously bid £1.8m for the company. Hallwood's new offer values the company's shares at 3.5p each.
Yesterday, rival bidder UKRD offered 3.25p per share, after The Local Radio Company (LRC) rejected a £1.25m bid it made in March.
Hallwood wants to buy the remainder of the company -- it already owns just over 28%.
Anthony Gumbiner, chairman of Hallwood, is also non-executive chairman of LRC.
Hallwood has previously said that it would let LRC remain publicly listed, and provide it with a £1m loan facility.
LRC owns a network of more than 25 stations including Isle of Wight Radio and Durham FM. It previously owned Jazz FM, but agreed to sell the station to former chief executive Richard Wheatly.
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