Born in Málaga, Alexis joined Getafe CF from Málaga CF for 2006–07, for €2.5 million. He had played for the Andalusia club for three years, after having spent as many with the B-team, two of those in the second division; he would first appear for the main squad of the latter on 15 February2004, playing eight minutes in a 5–2 home win against RCD Espanyol. Alexis scored the winning goal for Getafe against Real Madrid, in a 1–0 league home win on 14 October 2006, and was part of the league's best defence that season.
Valencia
In April 2007, Valencia signed Alexis to a €6.5 million deal at the Mestalla Stadium that ran until 2013, beating off competition from Real Madrid. After spending most of the campaign sidelined with a severe knee injury, he helped the team win the Copa del Rey, netting the second goal in a 3–1 win over former club Getafe in the final, after Juan Mata had scored the opener. On 14 September 2008 Alexis, who started the season as Raúl Albiol centre-back partner, netted in a 2–2 draw at UD Almería, but also spent two months in the sidelines due to a pubalgia ailment. He appeared in 24 games in the following campaign, helping the Che to a third-place in La Liga and former side Málaga avoid relegation as he headed home in the last-minute of the home fixture against CD Tenerife, which dropped down a level instead with that 0–1 loss.
Sevilla / Getafe return
On 24 August 2010, Alexis joined Sevilla FC for €5 million, signing a six-year contract with the Rojiblancos as a replacement for Arsenal-bound Sébastien Squillaci. He appeared in 21 league games in his first year as the team finished fifth and qualified to the UEFA Europa League. In the third game of 2011–12 – his first – Alexis salvaged a point for Sevilla with an 86th-minute header away against Villarreal CF. He would only be fourth of fifth-choice stopper for new manager Marcelino García Toral, however; in late February 2012, even though the winter transfer window had already closed, he was allowed to join former club Getafe on loan until the end of the season, as the Madrid outskirts side was immerse in a deep injury crisis to their defensive sector. The move was extended for the entire 2012–13. In the summer of 2013, Alexis agreed to a permanent four-year deal. He continued to be an undisputed starter when healthy, but missed several games due to suspension.
Alexis moved abroad again on 22 June 2018, joining Al-Ahli in the Saudi Professional League on a two-year contract. He returned to his country on 7 August 2019, however, agreeing to a two-year deal at newly promoted second division club Racing de Santander.
