The 18-year-old has caught the attention of a number of top European clubs after becoming a regular for Valladolid in the 2022-23 La Liga season.
The likes of Liverpool and Newcastle United have been strongly linked with a move for Fresneda, whose Valladolid contract does not expire until 2025.
Arsenal have also been credited with an interest, and the Premier League leaders are understood to have opened talks with Valladolid over a move for the 2004-born defender over the weekend.
According to journalist Guillermo Rai - via The Athletic - Arsenal have now agreed a €15m (£13.2m) fee with the Spanish side for Fresneda, but the Gunners will not conclude a deal that easily.
The report adds that German giants Dortmund, renowned for their development of young players, have also agreed to pay Valladolid the same amount to secure the right-back's services.
As a result, Fresneda must now choose between the Emirates or the Westfalenstadion for a January move, and he will supposedly come to a decision on Monday.
Whichever team wins the race for the Spaniard will loan him back to Valladolid for the remainder of the season, where he has already made 14 appearances in all tournaments.
Fresneda, who spent four years in the academy of Real Madrid, has started seven La Liga games for Valladolid in the 2022-23 season, but he was named on the bench for the weekend's contest with Atletico Madrid amid speculation surrounding his future.
The Spain Under-19 international came off the bench for the final 30 minutes of that 3-0 defeat, being deployed as a centre-back in what was Valladolid's fifth successive La Liga loss.
Arsenal have already signed Leandro Trossard from Brighton & Hove Albion this month and are close to sealing the signature of Spezia centre-back Jakub Kiwior.
The 22-year-old was in attendance at the Emirates to see the Gunners beat Manchester United 3-2 on Sunday, having completed his medical ahead of a transfer worth a reported £17.5m upfront, rising to £21m with add-ons.
Arsenal are expected to announce the signing of Kiwior within the next 24 hours, and Fresneda's summer arrival would open the door for Cedric Soares to head for the exit door.
The 31-year-old is now Mikel Arteta's third-choice right-back behind Ben White and Takehiro Tomiyasu, and Fulham are believed to be in talks over a January deal.
Arteta is apparently reluctant to let the experienced Cedric leave midway through the season, with the Portuguese seen as an important member of the squad behind the scenes, but his contract only runs for another 18 months.