According to Sky Sport, new sporting director Fabio Paratici is keen on both players, with Valdepenas representing the more advanced of the two situations.
Fiorentina are working on a permanent deal for the 19-year-old, but the transfer is complicated by Real Madrid's wish to retain 50 per cent of any future sale, similar to the structure used when Nico Paz left for Como, as well as new head coach Jose Mourinho's desire to assess Valdepenas in training before signing off on his departure, given the World Cup delaying the return of Real Madrid's international players.
Fiorentina fear a lengthy wait could allow Mourinho to change his mind, with Bologna also having made an approach for the Spanish defender.
On Oulai, the arrival of Arthur Atta from Udinese has not altered Fiorentina's midfield strategy, with Paratici viewing the Ivory Coast international as his preferred option to play in front of the defence. Talks remain far from an agreement, though Fiorentina intend to continue pursuing a player they see as capable of bringing balance and modern passing range to Fabio Grosso's midfield.
Fiorentina are also working on departures, with Dodo among the players expected to leave this summer. Contract renewal talks with the Brazilian full-back, whose deal expires in 2027, have stalled for some time, making a parting of ways increasingly likely. According to Sky Sport, Nottingham Forest have made an initial approach for the 27-year-old, while Napoli and Roma continue to monitor the situation in Serie A, ready to move if the right circumstances arise.
Valdepenas, a left-footed defender who stands 1.88m tall and can play across the back line, spent last season with Real Madrid Castilla in Spain's third tier and is contracted to the Bernabeu club until 2029.
Fiorentina moved for the player after already strengthening their defence this summer with the arrivals of Marco Viery and Radu Dragusin, and view Valdepenas as a versatile long-term addition to Grosso's back line should the deal with Real Madrid eventually be completed.