Manager David Moyes told the Everton website on Sunday: "I can only say that we have made an offer for him which was accepted and that's as far as I can say at the present time.
"I don't know what will happen but hopefully he will sign for Everton."
The website reported Beattie would have a medical on Monday and was poised to sign within the next 24 to 48 hours.
Beattie, who has five England caps, has been with Southampton since 1998, scoring 76 goals in 233 appearances. The previous record signing by Everton was 5.75 million pounds ($11 million) paid for ex-England midfielder Nick Barmby in 1996.
Southampton's new manager Harry Redknapp had indicated his readiness to sell Beattie to fund a fight against relegation. Southampton are 19th in the 20-strong league after losing again on Saturday, beaten 2-1 at Manchester City.
Fourth-placed Everton's ambitions suffered a setback when they lost 5-2 at Tottenham Hotspur. Despite their lofty position, they are averaging just over a goal a game with 25 goals from 21 matches.
Aston Villa, 1-0 winners over struggling Blackburn on Saturday, have also expressed an interest in Beattie as a potential strike partner for Colombian Juan Pablo Angel.
The Everton website said the Merseysiders and Villa had both offered six million pounds and it had been left to Beattie to decide which club he preferred.
Everton's spending power has been hugely boosted by last year's 20 million pounds ($38 million) sale of striker Wayne Rooney to Manchester United.
