The Switzerland international was previously considered one of the candidates to leave the Andalusian club, having struggled to enjoy the same prominence under Luis García Plaza.
That situation has changed considerably in recent weeks, with the 28-year-old winger working his way back into the manager's plans and making a stronger case for regular involvement.
According to Estadio Deportivo, Vargas is no longer contemplating an exit from the Ramón Sánchez-Pizjuán, while the club's position has also shifted. A departure that had looked possible is now considerably less likely, with both player and club increasingly comfortable with the direction things are taking.
His performance in the Copa del Rey has helped reinforce that change, but it was not the only factor behind the improvement. Vargas had already begun to establish himself more convincingly in the squad, showing García Plaza that he could make a useful contribution as the season developed.
The Swiss winger's progress has also come at an important time for Sevilla, with the coaching staff needing competition and depth across the attacking positions. His ability to operate out wide gives García Plaza another option, and the recent improvement in his involvement has strengthened his position.
Vargas had previously found opportunities harder to come by, prompting speculation that a move elsewhere might be the best solution for all parties. However, his renewed involvement has changed the calculation. Rather than looking for an exit, he now appears ready to compete for a more significant role in the second half of the campaign.
For Sevilla, keeping a player who is beginning to convince his manager would also avoid the need to find a replacement during the winter window. The situation is not necessarily a guarantee that Vargas will remain whatever offers arrive, but the expectation of an imminent departure has receded.
The Copa del Rey appearance has therefore become another important step in the winger's attempt to re-establish himself. After being linked with a January move, Vargas is now focused on making his place in García Plaza's plans more secure.