Liverpool and other clubs are making their returns to training now, but there is still plenty of transfer activity to get through this summer.

The Reds have started their pre-season preparations, with the first group of players returning to the AXA Training Centre on Saturday before the rest of the group joins them from Tuesday.

Those set to be back in training this week include new signings Alexis Mac Allister and Dominik Szoboszlai, and Jürgen Klopp will no doubt hope that at least one more new arrival will be joining them soon.

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The Liverpool boss still has some business to attend to this summer, but he’ll have to work his way around a market that is heating up across Europe.

Kylian Mbappé’s future will no doubt dominate headlines throughout the summer as his time at Paris Saint-Germain looks as though it could be coming to an end. And of course, whenever Mbappé is mentioned, Liverpool isn’t too far behind.

Here, Liverpool.com takes a scan around the other big sides in the Premier League and around Europe to take a look at the news going on at the other clubs.

Kylian Mbappé guarantee made after Liverpool ‘bid’

PSG feels Kylian Mbappé has an agreement in place to join Real Madrid in 2024, and is convinced he won’t join Liverpool, according to Fabrizio Romano.

Earlier this week, journalist Edu Aguirre sensationally claimed on El Chiringuito TV that Liverpool had made a $217m (£171m/€200m) offer for Mbappé. That has now been knocked back by Romano, who insists PSG can ‘guarantee’ it hasn’t received any bids from English clubs.

Liverpool.com says: No one really believed Liverpool had made a bid like that, did they? It always seemed too good to be true, and it was inevitable that someone would eventually knock back the claim. If Mbappé is going anywhere, it’s likely to be Real Madrid, although it would be galling to say the least if PSG loses him for free next year.

West Ham has been offered the chance to sign Arthur Melo from Juventus this summer, according to Tuttosport.

The Italian outlet claims Juve is looking to push the midfielder out of the club following his poor loan spell at Liverpool last season. Hammers boss David Moyes was reportedly offered the 26-year-old while holding talks over fellow Juventus midfielder Denis Zakaria.

Liverpool.com says: It’s hard to imagine any Premier League club wanting to sign Arthur after his spell at Liverpool. Having played a grand total of 13 minutes for the Reds’ first team, it’s fair to say his loan at Anfield was a complete flop, and West Ham would be taking a huge risk if it took the Brazilian on this summer.