Gameiro, who joined Atletico from Sevilla in the summer of 2016, has scored 27 times in 82 appearances for the Madrid giants over the last two seasons.
The striker only started 11 La Liga matches during the 2017-18 campaign, however, and his future at the Wanda Metropolitano has been called into question.
Last month, it was reported that Valencia had already agreed personal terms with Gameiro, and Alemany has confirmed that talks with Atletico are now underway.
"Yes it is true we have started talks with Atletico Madrid about Gameiro," Marca quotes Alemany as saying. "He is an accomplished striker and a very interesting possibility for us."
Gameiro has a contract with Atletico until the end of the 2019-2020 campaign.