It had been thought the 37-year-old was a victim of delayed concussion, having been struck on the helmet by a bouncer from England paceman James Anderson on Friday's second day.
But a London-based specialist said Rogers was suffering a balance problem in the inner ear.
Australia team doctor Peter Brukner said that while Rogers's condition was improving, he would remain in London for more treatment before a final decision was made on his availability for the third Test.
"Chris's condition continues to improve but he will remain in London for further tests and specialized treatment.
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"We are hopeful that he will be available for selection for the third Test."
After two overs' play on Sunday, Rogers crouched down by the side of the pitch and then sat motionless before eventually going off on 49 not out.
The left-hander played no further part in Australia's crushing 405-run win, which levelled the series at 1-1, having helped establish their strong position at Lord's with a Test- best 173 in the first innings.
Australia do have a back-up opener in their squad in Shaun Marsh while all-rounder Shane Watson, dropped from the side at Lord's following Australia's 169-run defeat in the first Test of the five-match Ashes in Cardiff, has had spells as an opener during his Test career.
Rogers missed Australia's recent 2-0 series win in the Caribbean with concussion after being hit on the head while batting in the nets.