Ashton intends to announce the tour party at Twickenham next Tuesday, although his plans for the first Test in Bloemfontein on May 26 have already been decimated.
Rugby Football Union elite rugby director Rob Andrew has said players involved in European finals a week before Bloemfontein will not be considered for that game.
It means around 30 players are unavailable, with Leicester tackling Wasps in the first all-English Heineken Cup final on May 20, and Bath facing European Challenge Cup final opponents Clermont Auvergne the previous evening.
Such chronic fixture congestion rules out the likes of Phil Vickery, Martin Corry, Harry Ellis, Joe Worsley, Josh Lewsey and Steve Borthwick.
Ashton has not yet indicated whether any of that sizeable group will fly to South Africa in time for the June 2 second Test in Pretoria.
Ashton said: "Now that the finalists for the Heineken Cup and European Challenge Cup have been confirmed, I have a clearer idea of the players available to me who I can consider for the summer tour to South Africa.
"I will spend the next few days considering all my options before making any final selection decisions after the forthcoming Guinness Premiership matches this weekend.
"I am absolutely delighted that Leicester Tigers and London Wasps have reached the Heineken Cup final, and that Bath Rugby are in the European Challenge Cup final.
"It is a tribute to all those involved at the clubs they have achieved that feat."
Ashton's selection problems are acute in the front row, where props Vickery, Julian White and Matt Stevens are ruled out of Bloemfontein, while Wasps loosehead Tim Payne is sidelined through injury and Sale Sharks' Andrew Sheridan is racing against time to be fit.
Hookers George Chuter and Lee Mears will not make it either, with Northampton prospect Dylan Hartley facing an RFU disciplinary hearing later on Tuesday that could see him land a lengthy ban.