The transfer window closed last week with Mbappe insisting he is yet to decide where he will play after this current deal with PSG concludes at the end of June, when he becomes a free agent.
On Saturday both ESPN and the Le Parisien daily newspaper reported, without naming their source, that the superstar striker would leave France and join the world's biggest club Real Madrid.
A source at the French club told AFP on Sunday, however, there had been no change in the longstanding deadlock.
He has "not informed the club of any decision", said the source, despite there being an agreement that the PSG president Nasser al-Khelaifi will be first to know when his decision is made.
Mbappe last spoke on the issue in cryptic terms in early January.
"I haven't made my decision, I haven't made my choice. But we have an agreement with the president (Al-Khelaifi) which means that all parties are protected," he told French television.
The France captain who is expected to head the Olympic team at the 2024 Paris Games added he would inform Khelaifi first and announce the news himself once any decision had been made.
PSG coach Luis Enrique, a former Real player, said Thursday, ahead of a game where Mbappe scored his 20th league goal of the season, that the player had revealed nothing to him personally.
What does appear certain is that Mbappe has signed no deal as yet but is, in fact, locked in negotiations with Madrid over the size of his salary, an issue where the Qatar-backed PSG could easily match Real.
Mbappe is paid some 70 million euros (£59.8 million) a year already and as a free agent will be able to negotiate a blockbuster signing-on fee on top of any salary increase.
PSG themselves appear to be pulling out all the stops to cling on to Mbappe'a's sublime skills after allowing Lionel Messi and Neymar to leave the capital.
Neither Messi nor Neymar have been missed as new arrivals such as Randal Kolo Muani and Marco Asensio have struck up an understanding with Mbappe.
If the 2018 World Cup winner and 2022 World Cup top scorer does join Madrid in July, he would join English sensation the 20-year-old Jude Bellingham and Brazilian strikers Rodrygo and Vinicius, one of whom would have to make way for the Frenchman.
