"I can confirm we have had a bid from Chelsea and that it will be rejected by us," Liverpool chief executive Rick Parry told BBC Sport on Tuesday.
Newspapers had reported the English champions had bid a British record 32 million pounds ($56.28 million) to prise the inspirational England midfielder away from his hometown club.
That would eclipse the 29.1 million pounds Manchester United paid to Leeds United for England defender Rio Ferdinand in 2002. Real Madrid are also rumoured to be interested in Gerrard.
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The 25-year-old is thinking over the proposal made after the club held talks with Gerrard and his agent on Monday.
Gerrard said nothing as he left Liverpool's Melwood training ground on Monday. Benitez earlier told a news conference he wanted the midfielder to stay at Liverpool for the rest of his career and could even become the club's next manager.
Liverpool are preparing to face Welsh part-timers TNS in their Champions League first round qualifier on July 13 after winning the trophy against AC Milan in May.
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