England may release Owais Shah from their warm-up in Baroda before the first Test against India so he can play for Middlesex in the Champions League.
Qualifiers for the lucrative Twenty20 competition are held straight after the final one-day international in Delhi.
Middlesex earlier said they were "very optimistic" that Shah and Andrew Strauss would be made available.
"If Owais isn't involved in the Baroda game we'd look to make him available," said England coach Peter Moores.
Shah and Strauss have both been included in England's squad for the Test series against India.
England initially refused Middlesex's request, preferring to keep Shah with the main squad for the three-day warm-up match in Baroda and the build-up to the first Test, to be played in Ahmedabad on 11 December.
But Moores has now softened his stance, adding: "We're looking at every possibility because we know it's a big tournament.
"The ECB is very keen for us as English representatives to do very well in the competition so they've been very supportive."
"So we'd look to make him available for those without affecting our preparation if he's involved in that first Test."
No decision has yet been made about whether Shah will be free to continue playing for Middlesex if they reach either the semi-finals on 8 and 9 December or the final the day after as that would interfere with the build-up to the Test.
It is considered less likely that Middlesex will be able to prise Strauss away from the England setup, but Middlesex chief executive Vinny Condrington earlier said he had received "very positive noises" about the pair from the England and Wales Cricket Board.
"The ECB has been absolutely fabulous," Codrington told BBC Radio London 94.9.
"We've had a close dialogue with them throughout and we continue to do so with regard to them (Strauss and Shah).
"We are optimistic that they will be made available to us to play in the Champions League.
"The ECB is very keen for us as English representatives to do very well in the competition so they've been very supportive. But we won't know for a while - at least until we get over there."
The lucrative Champions League event involves eight teams from around the world and takes place from 3-10 December, with the final on the eve of the first Test between England and India in Ahmedabad.
The winners will earn $3m (£1.86m), so Middlesex want to have two of their best batsmen available if at all possible.
Australia, South Africa and India each have two teams in the competition with Middlesex and Pakistan's Sialkot Stallions making up the numbers.
There were originally two places on offer for England, but Kent, beaten by Middlesex in the Twenty20 Cup final, were refused entry because two of their players have appeared in the unsanctioned Indian Cricket League.
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