The middle-order batsman has been following a rehabilitation programme since suffering the calf injury that prevented him fielding in the second innings of last week's second Test win at Lord's.
The 33-year-old still has time to prove his fitness for the next match at Old Trafford, which begins on Thursday, but England may need to add cover as they name their initial squad on Sunday.
England are hoping to secure series victory in Manchester after beating the Australians in the opening two Tests of the five-match series at Trent Bridge and Lord's.
Nottinghamshire's James Taylor, having been drafted into the Sussex side to face Australia at the England and Wales Cricket Board's request this week, would seem the most likely cover option.
Taylor, 23, played two Test matches against South Africa last summer but was overlooked for the tours of India and New Zealand and subsequently fell behind Nick Compton and Joe Root in the pecking order.
He boasts good form this summer having scored 824 runs in 15 County Championship innings with an unbeaten double century against his temporary side, Sussex, in June.
He was kept waiting for his opportunity to further press his claims on the opening day of the tour match at Hove, however, as the Australians batted throughout.
One potential England player did get into the action as left-arm spinner Monty Panesar took three for 65 against the tourists.
Old Trafford may not have staged a Test since 2010 due to extensive ground redevelopment - including a 90-degree rotation of the square - but its reputation for spin endures.
That means both sides could consider bringing in a second slow bowler, and Panesar has long been regarded as the back-up to Graeme Swann.
The 31-year-old has not played a home Test since Australia's last visit in 2009 - when he shared in a memorable final-wicket partnership with James Anderson at Cardiff - but he has remained in England's thinking.
He has played nine away Tests in that time, including all three in New Zealand in March.
Adding Panesar could mean leaving a seamer out of the squad.
Steven Finn and Graham Onions could be the most vulnerable having not made the final XI to play the second Test. Finn played at Trent Bridge but lost his place to Tim Bresnan at Lord's.
If England decide against a second spinner and instead decide to rejig their pace options, Surrey's Chris Tremlett is thought to be in good position for a recall.
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