Roberts, a centre, is out of contract with Bath at the end of the season after spending two years with the club, having earlier played for Harlequins. He was reportedly in negotiations with the Crusaders but that fell through after the All Blacks lost their World Cup semifinal to England.
South African media reports said funding has been made available from a third party which would allow Roberts to play in Cape Town.
A veteran of 97 Tests, 94 of them for Wales and three for the Lions, the 33-year-old also has experience with Cardiff Blues in Pro14 and Racing Metro in France's Top 14.
The Stormers lost World Cup-winning second five-eighths Damian de Allende when he switched to Japan's Wild Knights before joining Munster on a two-year deal.
Media in South Africa were alerted to a possible resolution to Stormers coach John Dobson's comment that they had a plan to deal with what he described as one potential problem area in their side, in the midfield.
Stormers mid-fielder Dan du Plessis is still suffering injury problems, while young signing Michael Hazner, who was a star for Griquas in the Currie Cup, has played more at outside centre and Ruhan Nel will not be available should the Stormers make the playoffs as he will be with the Blitzbok Sevens at the Olympic Games.
It has been reported by SuperSport in South Africa that Roberts will have a brief to help develop exciting Stormers first five-eighths Damian Willemse and du Plessis when he returns.
The timing of Roberts' switch has been unclear but it has been suggested it could happen as soon as this week.
It would depend on whether Bath would give Roberts an early release. They are sixth in the Premiership, five points off the top four. However, the return of former Chiefs centre Jackson Willison from a concussion layoff may help Roberts' cause.
Willison made his first start of the season in the weekend's 19-25 loss to Harlequins in the Champions Cup and was rated Bath's best player.