PARIS (AFP) - A dizzying transfer window that has seen Lionel Messi and Cristiano Ronaldo change clubs went into its final hours on Tuesday (Aug 31), with the issue of whether Kylian Mbappe could make a blockbuster move from Paris Saint-Germain to Real Madrid still unresolved.

The future of Mbappe dominated the final day of a remarkable window in which Messi moved to PSG after spending his entire career at increasingly cash-strapped Barcelona and Juventus' Ronaldo made a sensational return to former club Manchester United.

While the moves for 34-year-old Messi and 36-year-old Ronaldo represented a shift in world football's tectonic plates, the future of 22-year-old Mbappe is potentially more significant for the sport in the long term.

Already a World Cup winner, Frenchman Mbappe's goals could vastly improve the fortunes of Real, who were beaten to the Spanish title by local rivals Atletico Madrid last season.

But having signed Messi to line up alongside Neymar and Mbappe in a formidable attacking trio, Qatari-owned PSG have been fighting to keep their striker in the face of a sustained offensive from Real.

A PSG insider denied reports that the Spanish giants, having had bids of €160 million euros (S$254 million) and €180 million rejected, had made a third bid of €200 million.

If the Paris-born Mbappe stays, and with each passing hour that prospect looked more likely, then PSG will believe they have their strongest chance ever of winning an elusive Champions League.

Apart from the addition of Messi, they have also signed four-time Champions League winner Sergio Ramos from Real and one of the world's top goalkeepers, Gianluigi Donnarumma, on a free transfer from AC Milan.

They also strengthened their midfield with Georginio Wijnaldum from Liverpool and Morocco right-back Achraf Hakimi, who shone for Inter Milan last season.

Ronaldo back to adoring Old Trafford

Ronaldo, meanwhile, sealed a return to an adoring public at Old Trafford, where he rose to world-class status in a first stint from 2003 to 2009.

"This is absolutely 100 per cent the stuff that dreams are made of," Ronaldo posted on Instagram on Tuesday when his move from Juventus was officially completed.

After also adding England winger Jadon Sancho for £73 million from Borussia Dortmund and French centre-back Raphael Varane from Real, United manager Ole Gunnar Solskjaer has little excuse if he fails to land a trophy this season.

Champions League holders Chelsea spent a club record £97 million to bring Romelu Lukaku back to Stamford Bridge from Inter Milan and let Tammy Abraham move to Italy to join former boss Jose Mourinho at Roma.

Inter brought in Denzel Dumfries, the Netherlands wing-back from PSV Eindhoven who starred at Euro 2020 in the summer.

Premier League holders Manchester City, another club bidding to win a first Champions League title, signed Aston Villa playmaker Jack Grealish for £100 million (S$185.2 million) to further strengthen a squad that has lost Sergio Aguero to Barcelona.

But City's pursuit of Harry Kane ended in frustration when the England captain decided to stay at Tottenham, having tried unsuccessfully to force a move.

Liverpool reinforced their central defensive options by acquiring Ibrahima Konate from Leipzig, but have otherwise largely focused on signing established stars such as Virgil van Dijk and Andy Robertson to new contracts.

Of all the Premier League clubs, Arsenal looked most likely to make moves in the transfer market as the clock ticked down, having made a disastrous point-less start to the season.