Everton's top scorer last season was Chelsea's Romelu Lukaku, while Lacina Traoré made just one start during his spell on loan from Monaco. Rémy himself excelled during a season-long loan spell at Newcastle.
Rémy has an £8 million buyout clause inserted into his contract at parent club Queens Park Rangers, which Everton should be able to afford.
The caveat is Rémy, like Lukaku, said earlier this season he was eager to move to a club who will offer Champions League football - which Everton don't and Arsenal do. The France striker, named in Didier Deschamps' World Cup squad on Tuesday, was at the Emirates Stadium for the Gunners' final game of the campaign as a guest of Bacary Sagna, who, ironically, could leave Arsenal.
Liverpool are ready to make an improved bid for Southampton midfielder Adam Lallana after their initial bid was rejected. The Reds want to conclude the deal before the World Cup starts.
The Guardian, however, say Lallana may have to submit a transfer request. This is when the ludicrous "loyalty bonus" usually influences a player's thinking.
Arsenal and Manchester City are both linked with moves for Real Madrid winger Angel di María, arguably the most improved player at the club this season.
Despite the arrival of Gareth Bale, Di María remains an integral part of Real's side and should start the Champions League final, despite both the Welshman and Cristiano Ronaldo's presence.
Alexis Sánchez's mixed three years at Barcelona should come to an end this summer, and Arsenal are apparently willing to offer £24m for the Chilean.
Former Udinese man Sánchez is also wanted by Juventus, say AS.
And Manchester United had a deadline day bid rejected for Sami Khedira last year, but the German is now being targeted by Roma, as well as Fiorentina and Chelsea, claim Bild.