The 21-year-old Australia midfielder was the subject of a £600,000 bid from Rotherham, who were promoted to English football's second tier via the play-offs in May.
Luongo has two years remaining on his contract with Swindon, while the third-tier club would reportedly owe the Australian's former employers Tottenham a percentage of any funds received, due to a sell-on clause in the £400,000 deal that brought him to the County Ground in 2013.
"He's not going, and I don't know if we would sell him," Swindon manager Mark Cooper told the BBC.
"I don't think there's any pressure.
"With all due respect to Rotherham, I don't think Mass would go there. It was a fantastic offer but I think he's worth more than that."
After making his full international debut off the bench against Ecuador in March, Luongo was included in Australia's squad for the World Cup but didn't get on the field during any of his country's three games in Brazil.
Having spent time on loan at Swindon in the 2012/13 season, Luongo completed a permanent move in August of last year and made 44 starts in League One, scoring six goals.
