The 28-year-old has been instrumental for the Springboks this season and was recently also shortlisted as an IRB World Rugby Player of the Year nominee.
According to the Express.co.uk website, Bath are lining up Vermeulen as a second marquee player alongside Wallaby scrumhalf Will Genia.
The deal, which would be worth £450 000 (about R7.8m) per season, would make him the second-highest earner in the Premiership behind new rugby league recruit Sam Burgess.
Other players nominated alongside Vermeulen for the IRB World Rugby Player of the Year are his compatriot Willie le Roux, Ireland's Jonathan Sexton, and All Blacks Brodie Retallick and Julian Savea.
Next year's Rugby World Cup, to be staged in England and Wales, runs from September 18-October 31.