Talks between the two clubs are continuing, with Álvaro Arbeloa's side looking to strengthen their defensive options before Tuesday's deadline.
Rațiu is primarily a right-back but is capable of playing in other positions across the backline.
Any deal is likely to hinge on Fulham's willingness to meet, or negotiate down from, the €25m release clause in his contract - a figure well above his estimated market value of around €18m, with Rayo having shown no appetite to sell for less.
Romania-born Rațiu has spent almost his entire club career in Spain since joining Villarreal's academy, aside from a loan spell at Dutch club ADO Den Haag. He left Villarreal for Huesca before making his La Liga debut following a move to Rayo Vallecano in 2023, where he has since become one of the division's more consistent performers outside Spain's traditional top three, also featuring regularly for the club in the UEFA Conference League.
Rayo extended his contract to 2030 after signing him permanently from Villarreal last year, and personal terms between the player and Fulham are already understood to be agreed, leaving a club-to-club resolution on the fee as the final obstacle.
Arbeloa, who replaced Marco Silva as Fulham boss this summer, is keen to add further reinforcements before deadline day. The Cottagers have already signed striker Gonzalo García and attacker César Palacios from Real Madrid, along with midfielder Shea Charles from Southampton, and have made forward Jonah Kusi-Asare's loan move from Bayern Munich permanent.
Should Rațiu arrive, he would compete for the right-back spot with Kenny Tete and Timothy Castagne.
Fulham suffered a 3-2 home defeat by rivals Chelsea in their Premier League opener, but responded with a 3-0 win over AFC Wimbledon in the Carabao Cup. Nottingham Forest have also made enquiries about Rațiu's availability, while Liverpool have been linked with the defender at various points throughout the year, adding further urgency for Fulham to get a deal over the line before the window shuts.
Rayo rejected an €18m bid for Rațiu from an unnamed Premier League club last year, underlining their determination to secure his full release clause or keep him this summer, and any fee in the region of €25m would rank among the biggest sales in the Madrid club's history.