The 31-year-old striker has seen his stock rise considerably since returning to his roots in the summer of 2015.
An ill-fated stint at Liverpool in 2013-14 had knocked his confidence, but a return to prolific form in front of goal has been enjoyed back at Celta.
Aspas has netted 67 times in 127 appearances during a second stint with the club that helped to put him on the map.
Those efforts saw him form part of Spain’s squad at World Cup 2018, while also sparking talk of another potential big-money move to a European heavyweight.
Aspas has never pushed for a switch, though, telling Marca: “I personally did not call another team. It is true that several got in touch with my brother and my agent.
“I have always been honest, anyone interested had to come to an agreement with Celta first and then we would see if it interested me later.
“There were important teams, interest from Real Madrid and Atletico came out in the press and I imagine it was true.
“The club did not say anything to me. I suppose there were talks and nothing went any further.”
Rather than looking for a move elsewhere, Aspas continues to plan for the long term at Celta.
He committed to a new contract in April 2017, with the options within that agreement set to take him through to 2022.
“I have always seen myself at Celta for as many years as possible,” added Aspas.
“That is why I signed a contract extension.
“I hope to speak with the club in the future and to continue for as many years as possible.”