Shorting a stock is a bet that the share price will fall.

GameStop had around 140% short interest at its peak in January, meaning more shares were shorted than the company had outstanding.

"The ability for the same share to be shorted an indefinite number of times is somewhat of a pathology and that should be fixed," said Robinhood Chief Executive Officer Vlad Tenev.

He called for a modernization of the market's infrastructure so shares can properly be tracked once they've been loaned out to be shorted, which does not currently happen.

The GameStop saga could also dampen industry demand for shorting stocks going forward, said Melvin's CEO Gabe Plotkin.

Melvin had been short GameStop since 2014. It suffered massive losses as retail investors piled into GameStop in January, driving its price up 1,400% and creating a "short-squeeze," where short sellers were forced to buy the shares back at a higher prices to close their positions, adding to the upward pressure on the stock price.

Citadel made a $2 billion investment in Melvin on Jan. 25, which closed its GameStop position on Jan. 27. People familiar with the fund said it lost almost 30% in the first three weeks of January.

Citadel CEO Ken Griffin said of short-selling reforms that as far as legislative priorities that could improve the markets go, "this doesn't make the top 100 list."

"The short interest in GameStop was exceptional and I'm not sure it's worth us delving into legislative corrections for a very unique situation in terms of the extreme sides of the short interest," he said.

(Reporting by John McCrank; Editing by Megan Davies and Christopher Cushing)

By John McCrank