Goal understands that Perez has undergone a medical at West Ham, while Ospina will hold talks with Turkish giants Besiktas over joining them before the summer transfer window closes.
Fiorentina are looking to offload several players this summer in order to trim their squad and the Colombia global is believed to be on the cull list.
The midfielder previously had a stint at Aston Villa and made 48 Premier League appearances for the club before they were relegated to the Championship in 2016.
With further midfield signings on the agenda, West Ham could be tempted to cash in.
The Spain worldwide was loaned out to his former employers last season.
Steve Bruce's side are keen on signing Snodgrass on a permanent basis and, although the Guardian states West Ham have no interest in a sale, the promotion hopefuls could lodge a cheeky bid before this afternoon's deadline.
West Brom have emerged as surprise contenders in the race to sign Fiorentina midfielder Carlos Sanchez, with West Ham also keen.
"Listen, it's great first and foremost to come back and see them, but I'm a West Ham player".
West Ham have continued their £100million summer spree by signing Lucas Perez - and will swoop for "The Rock" next.