Crystal Palace have agreed a fee with Everton for striker Oumar Niasse, and have also bid £23m for Manchester City defender Eliaquim Mangala.
Niasse, who had also been a £10m target for Brighton, spent last year at Hull, where he scored five goals in 20 games.
Everton paid Lokomotiv Moscow for £13.5m for him 18 months ago, but the Senegalese made just five appearances.
Palace are also hopeful of signing Frenchman Mangala, 26, but BBC Sport understands a deal is unlikely.
Liverpool’s Mamadou Sakho was Palace’s first choice and the France international, 27, is keen to return to Selhurst Park, where he enjoyed a successful loan spell last season.
But despite Palace improving their offer Liverpool seem unwilling to lower their asking price of £30m.
BBC Sport’s David Ornstein
Palace have had their Niasse bid accepted but it’s certainly not a done deal and the club are still pursuing alternatives.
Mangala is also a target of West Bromwich Albion, who will only let Jonny Evans leave if they have a replacement, and Mangala is their preferred candidate.
With City looking to sign Evans and the Northern Ireland defender keen to move to Etihad Stadium, that deal would appear straightforward.
However, it is complicated by Evans travelling to San Marino with Northern Ireland on Thursday morning and by Mangala indicating he would prefer a move to Inter Milan – the likelihood of that has increased since Inter’s move for Arsenal defender Shkodran Mustafi broke down.
Mustafi’s representatives also held talks with Juventus, only for the Italians to sign his Germany team-mate Benedikt Howedes on loan from Schalke.
Mustafi will therefore stay at Arsenal – a situation that suits neither him nor them – and that means the Gunners dropping their own interest in Evans, who is also a target for Leicester City.
Meanwhile, aside from the unchanged Alexis Sanchez situation, the only significant departure from Arsenal is set to see striker Lucas Perez leave just a year after joining from Deportivo La Coruna.