The Competition and Markets Authority (CMA) said they can expect to face fines if they are found to have broken the law.
The CMA alleges that Elite Sports and JD Sports fixed the retail prices of a number of Rangers-branded replica kits and other clothing products from September 2018 until at least July 2019.
It also said that Rangers Football Club took part in the alleged collusion, but only to the extent of fixing the retail price of adult home short-sleeved replica shirts from September 2018 to at least mid-November 2018.
All three are alleged to have colluded to stop JD Sports from undercutting the retail price of the shirt on Elite’s Gers Online store, according to the CMA.
Michael Grenfell, executive director of enforcement at the CMA, said: “We don’t hesitate to take action when we have concerns that companies may be working together to keep costs up.
“Football fans are well-known for their loyalty towards their teams.
“We are concerned that, in this case, Elite, JD Sports and, to some extent, Rangers, may have colluded to keep prices high, so that the two retailers could pocket more money for themselves at the expense of fans.”
JD Sports Fashion said it plans to book at hit of around £2 million in preparation for a fine from the CMA and legal costs in its annual results for the year to January 29, which it will release “shortly”.
It said: “The CMA’s findings are, at this stage, only provisional and the group will now review them with its advisers.
“The CMA will consider any representations that are made before issuing its final findings.
“As the CMA has noted, JD has co-operated fully with the CMA and, provided this continues, JD will receive a reduction on any financial penalties that the CMA may decide to impose.”
Rangers FC said it “treats this matter very seriously”.
“Rangers will review in detail the CMA’s preliminary findings and will be submitting its response to the CMA in due course,” it added.