The approach to the Bayer Leverkusen defender follows comments from Grimaldo himself, in which he made clear his long-standing wish to return to Spain.
"I want to return to LaLiga, that's one of my goals," Grimaldo said.
He stressed that his time in Germany had been positive, but that a return home remained a long-term ambition.
"I'm very happy at Bayer Leverkusen, but I've always said that I want to return to LaLiga, and at some point I will."
According to reports, Atletico Madrid's interest in the 30-year-old has firmed up considerably in recent days.
Grimaldo, who came through Barcelona's youth academy before moving to Benfica and then Leverkusen, has spent three seasons in the Bundesliga.
He scored 14 goals and provided 14 assists in 46 appearances across all competitions during the 2025/26 season.
Atletico's pursuit of a left-back has also taken in Chelsea's Marc Cucurella, a fellow Spain international.
Cucurella, 27, has three years remaining on his contract at Chelsea, which runs until 2029.
Reports suggest his salary demands would make any deal for the Chelsea defender considerably more complicated than a move for Grimaldo.
Grimaldo's contract at Leverkusen runs until 2027, a structure that reportedly makes him the cheaper and more straightforward option of the two for Atletico to pursue.
Grimaldo has previously discussed interest from elsewhere in Spanish football without any of it translating into a concrete deal.
He has acknowledged conversations with both Real Madrid and Barcelona in the past, neither of which progressed to a transfer.
Real Madrid instead signed Alvaro Carreras as their left-back option, while talks with Barcelona did not advance further.
Speaking before his first World Cup appearance for Spain, Grimaldo reiterated that contacts in the transfer market do not always lead anywhere concrete.
He described previous interest from Atletico as having amounted to little in practical terms, despite conversations taking place.
This summer, though, the position appears more advanced, with Atletico viewing Grimaldo as the more realistic of their two left-back targets given his contract situation and the financial complexity surrounding Cucurella.
For a player who has long made his preference for a return to Spanish football clear, this represents the most concrete movement yet towards that goal, even if Atletico's final choice between Grimaldo and Cucurella remains unresolved.