According to ''the Daily Telegraph'', Flower, along with Duncan Fletcher, are among the shortlisted candidates for the post vacated by Kirsten after India's World Cup triumph.
The ECB, which is determined to hold on to Flower after he guided England to the Ashes and World Twenty20 triumphs, is doing all it can to prevent the former wicketkeeper from being lured by India.
"Andy Flower has been offered a new three-year contract as the England and Wales Cricket Board attempts to head off any moves for their highly rated coach from India," the report said.
"Telegraph Sport understands Flower is due to meet Hugh Morris, the managing director of the England team, at the end of the month to discuss his long-term future and the direction of the England set-up. It is thought that Flower is on a rolling staff contract which offers the same protection rights as any other full-time employee."
Flower, who has been on a holiday after England were knocked out in the quarterfinals of the ODI World Cup, has been non-committal about his future.
After the Ashes series, Flower had said that "personally I don''t look much further forward than a few months".
Like ECB, even the English players are keen to have Flower for another term.
"I can''t sing his praises highly enough," said wicketkeeper Matt Prior.
"He has been fantastic. The main thing I love about Andy is he is honest. He is a good human being. There are no politics. He just wants to win. Any decision he makes is because he thinks it gives England the best chance of winning.
"There is nothing else to him. That is really important.
The other thing is he backs his players 100 per cent. To walk out on the pitch knowing your coach is backing you and giving you that support and responsibility to know and trust your game is huge," he added.