However, both Newcastle and West Ham are also understood to be keen on landing the forward, while Leicester have been linked.
And Sky Sports claim QPR are urging suitors to open talks as manager Chris Ramsey seeks an immediate replacement striker before the transfer deadline shuts.
At the moment, Austin is in line to start for Rangers in their opening Championship cash against Charlton this weekend.
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QPR's Charlie Austin is set to play against Charlton this weekend
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Newcastle were frontrunners to sign him at the back end of last season but manager Steve McClaren has instead brought in Aleksandar Mitrovic and winger Georginio Wijnaldum to bolster his attack.
The Hammers, meanwhile, have so far resisted to spend money on forward recruits.
As for QPR, they have so far spent over £3.7m on three new signings this summer, while left-back Paul Konchesky was confirmed as a loan arrival from Leicester this week.