Tshibola cost Villa a reported £5 million from Reading in the summer, but has played just seven times for his new club and has not appeared for the first team since Steve Bruce's maiden game in charge more than two months ago.
Aston Villa's Aaron Tshibola
The 21-year-old is now said to be eyeing a temporary move to a club in Europe, with Rangers an appealing option.
The Gers tore up Joey Barton's contract last month, while Matt Crooks has barely featured since his move to Ibrox from Accrington Stanley in the summer.
Though there is no suggestion within the report that Rangers are interested in Tshibola, the imposing midfielder could be a useful option if Crooks were to leave on loan.
Ibrox boss Mark Warburton has a strong knowledge of English youngsters, having coached at Watford and Brentford in his homeland and helped to set up the NextGen Series for under-19s.
Rangers manager Mark Warburton
Rangers have already been linked with a move for teenage Aston Villa striker Rushian Hepburn-Murphy.
Would Tshibola be a good signing for Warburton's Rangers?