After sacking Xabi Alonso barely six months into his job, Florentino has seen the coach's replacement, Alvaro Arbeloa, lose on debut as Real were knocked out of the Copa del Rey by Segunda Division Albacete in midweek.
The Sun says Florentino has plans to bring two major identities from the Premier League to Madrid to revive their fortunes.
Axed Chelsea manager Enzo Maresca is being viewed as an ideal long-term appointment. Despite his demise at Chelsea, Maresca enjoys a growing reputation across Europe after winning the Club World Cup and Europa Conference League titles with the Blues last year.
Along with the Italian, Florentino also intends to launch a bid for Manchester City star Erling Haaland.
The Real president is close to Haaland's agent, Rafaela Pimenta, and is kept up to date on the player's plans.
Despite Haaland signing a new deal to 2034 last season, Florentino does hold the belief he can convince City to part with the centre-forward this coming summer.
Any move, however, would be dependent on selling Vinicius Junior for massive money at the end of the season.