England striker Welbeck and Czech midfielder Rosicky would stay in London to continue rehabilitation on knee injuries, the club said on Thursday, while Sanchez has been given extended leave after helping Chile win the Copa America last week.
Colombia goalkeeper David Ospina, linked with a move away from the club after the arrival of Cech from London rivals Chelsea, has also been given leave after the Copa America and will miss the trip.
Versatile defender Calum Chambers will travel to Singapore in the 27-man party, though, after seeing little action at the European under-21 championships.
"Calum has decided to shorten his holiday and come back on Friday," Wenger told Arsenal.com. "He didn't play in the under-21s and needs preparations.
"Welbeck isn't completely recovered from the problem he had (at the end of last season). He's not back in full training so he will stay behind.
FA Cup winners and 13-times English league champions Arsenal will take on a Singapore Select XI on Wednesday in their first match of pre-season at Singapore National Stadium.
Should they win that fixture, they will play on Saturday in the final against the winners of Wednesday's other fixture between English rivals Stoke City and Everton.
(Reporting by Patrick Johnston; Editing by John O'Brien)
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