Sporting Lisbon have told Sandro they want a quick decision on whether he wants to sign for them.
The Brazilian midfielder, 27, has been discussing a potential move to Sporting from QPR.
But the Portuguese club have made it clear they will turn their attention to other targets within days if an agreement is not reached.
Sandro has made just 28 league appearances since joining Rangers from Tottenham for £6m in 2014. He ended last season on loan at West Brom.
Meanwhile, QPR are interested in Legia Warsaw midfielder Ariel Borysiuk and are pursuing deals for Brentford left-back Jake Bidwell, Huddersfield defender Joel Lynch, Metz winger Yeni Ngbakoto and Lille forward Sehrou Guirassy.
Rangers have also spoken to Belgian club Oud-Heverlee Leuven about a potential deal to sign John Bostock.
Former Tottenham midfielder Bostock, 24, is keen to secure a return to England this summer.
The R’s begin their pre-season campaign with a friendly at Aldershot Town on 1 July.
This post was last modified on 03/06/2016