The centre-back has been relegated back-to-back with Blackburn Rovers and Birmingham City, but Southampton are determined not to let that happen for a third time.
Rovers had hoped to keep the defender, but a bid of £3.5 million is expected to be accepted.
Saints boss Nigel Adkins has high expectations for his side this season and his enthusiasm could convince Dann that this season will be third time lucky.
Source: DSG