AS claims that two La Liga giants have already made an enquiry to sound out the availability of the 21-year-old midfielder ahead of a potential future move.
The Spanish publication add that Tottenham Hotspur and AS Roma have also expressed an interest in signing the player during the current January transfer window but Betis hope the midfielder to snub all them and instead sign a new long-term deal at the Benito Villamarin Stadium.
Fabian progressed through the youth ranks of the Andalucian side before being handed his first-team debut in December 2014 when Betis were in the second division.
The towering midfielder struggled to breakthrough into the first-team in the following campaign and last season was sent on loan to Elche to complete his development.
He returned to Betis in the summer and has since proved to be one of the sensations of La Liga during the opening half of the season, scoring two goals in 15 appearances; earning him a place in the Spanish Under-21 side.
AS claims that Fabian's impressive form in La Liga have put both Barcelona and Real on alert ahead of making a future move to secure his services.
Tottenham and Roma are also said to be monitoring the situation after discovering that the talented midfielder has a €15m (£13.2m, $18.4m) release clause in his current contract.
But the Spanish publication claims that Betis have quickly reacted to the interest of Barcelona and Real by offering Fabian a new lucrative deal which will increase his current clause to €40m.
Earlier this week the midfielder said that he planned to stay at Betis for the long-term but AS claims that the Fabian wants his clause to be closer to between €25m and €30m in order to ensure he remains available for a future move away.
"My agents are currently negotiating with Betis and I really hope we can renew," Fabian told Cadena Ser El Larguero. "My dream is to stay at the club and if this must happen through a renewal, then it will."
Betis are already familiar with the situation after in the summer another pearl from their academy, Dani Ceballos, also attracted the attention of Barcelona and Real.
The Andalucians then tried then to tie Ceballos down to a new deal but were eventually unable to prevent his departure after Los Blancos triggered his €15m release clause to lure him to the Santiago Bernabeu.
Real also beat Barcelona to the signing of Vinicius de Oliveira Junior and Theo Hernandez during the summer transfer window but the Brazil starlet remains on loan at Flamengo while the France left-back has struggled to make any impact under Zinedine Zidane during his first months at the club.