Asensio, 21, has made an impressive start to the season, scoring four goals in six games in all competitions for Madrid.
The Spain international, who arrived at Madrid from Mallorca in 2014, is considered one of the brightest young talents in the world.
Asensio was linked to PSG, among other clubs, last month, but the attacker is happy at Madrid.
"I don't know how much I'm worth... I guess what my [release] clause says," he told COPE.
"If I would go to PSG? No, not really, because I'm very happy here."
Asensio was signed by Madrid for a reported €3.9 million ($5.8 million AUD) in late 2014, but it could have been so different.
He recalled Barca's interest in his services, with Asensio's agent – Horacio Gaggioli – having previously said Madrid's rivals missed their opportunity earlier in 2014.
"I started with the first team of Mallorca and Barca appeared," Asensio said.
"The end is the destination, not Barca, and I was delighted to be at Real Madrid and to defend this shirt.
"When Horacio called me and told me Real Madrid were interested, I said I just wanted to play there."