The move comes after it emerged that Mr Cowgill was filmed meeting Barry Bown, his counterpart at Footasylum.
JD Sports bought Footasylum for £90m in April 2019 but last week was ordered to sell it by the competition watchdog.
There are concerns that the meeting may have contravened competition rules. Both firms deny any breach.
The Competition and Markets Authority (CMA) has been examining the deal since May 2019 and put in place an enforcement order that states that meetings between bosses of the two companies are allowed, but they must not share any confidential or commercially sensitive information.
News of the meeting came to light in an article published in the Sunday Times.
JD Sports said on Monday: “Peter Cowgill has known Barry Bown on a business and personal basis for over 25 years.
“As a result, it is not unusual, or in any way suspicious or illegitimate, for them to meet from time to time, including in relation to the ongoing review by the Competition and Markets Authority (CMA) of JD’s acquisition of Footasylum Limited.
“The Sunday Times omitted to report on the positive obligation that JD has under the terms of the Interim Enforcement Order to take all reasonable steps to encourage key staff of the Footasylum business (which includes Barry Bown) to remain with the business.”
JD Sports said the CMA had been fully informed about the meeting, which took place on 5 July.
The company also said: “It is disappointing that the Sunday Times has not reported in a more balanced way on the highly irregular and potentially illegal covert surveillance undertaken by a third party for their own interests,” the statement continued.
“JD hopes that a regulator, tasked with acting in the wider public interest, is able to more critically regard the actions of the third party for what they are.”
A CMA spokesperson said: “These rules are put in place to protect consumers and other businesses operating in that market as we investigate a merger. We take compliance very seriously and thoroughly investigate any potential breaches. Where there is clear evidence that a breach has occurred, we do not hesitate to take action.”
Last week, following an in-depth investigation, the CMA ruled that the takeover of Footasylum by JD Sports could lead to a “worse deal” for customers and it would have to sell the chain.
But JD Sports hit back, calling the decision “inexplicable” and “beyond logic”.
Mr Cowgill suggested that the CMA was in “a minority of one in reaching this conclusion”.