A product of Atlético Madrid's youth system, Suárez was born in Alcobendas, Madrid. He first appeared with the first team on 6 November 2005, playing four minutes in a 0–0 draw at Sevilla FC and going on to make a further three La Liga appearances during the season, including two 90-minute games. From 2006 to 2008, Suárez served two Segunda División loan stints, being an important element in Real Valladolid's 2007 top flight return and spending his second year at RC Celta de Vigo. In August 2008 he was purchased by RCD Mallorca, signing a four-year deal that left Atlético the possibility of reacquiring the player. After two seasons appearing regularly, the rebuy clause was activated, and Suárez returned to the Colchoneros. In his debut campaign in his second spell, he battled for first-choice status at holding midfielder with Brazilian Paulo Assunção. He netted his first official goal for the club on 10 April 2011, in a 3–0 home win against Real Sociedad. On 10 August2014, Suárez was knocked unconscious in a friendly against VfL Wolfsburg, after teammate Cristian Ansaldi's hip hit his head. He suffered a "traumatic brain injury" and stayed for treatment in Germany, while the rest of the team returned to Spain. However, on 19 August, he played the entire first leg of the Supercopa de España, a 1–1 draw away to Real Madrid. Suárez scored his second competitive goal of 2014–15 on 17 March 2015, netting through a 27th minute deflected effort for the only goal against Bayer 04 Leverkusen in the UEFA Champions League's round-of-16. He also converted his penalty shootout attempt, in an eventual 3–2 win.
Fiorentina
On 24 July 2015, Suárez signed for Serie A club ACF Fiorentina, with Stefan Savić moving in the opposite direction. He appeared in only 13 competitive games during his six-month tenure, his maiden league appearance occurring on 23 August in a 2–0 home win over A.C. Milan ; his sole goal for the Viola came on 1 November, in a 4–1 rout of Frosinone Calcio.
On 30 January 2016, after weeks of negotiations, Watford announced the signing of Suárez on a four-and-a-half year contract, for €4 million transfer fee. His first Premier League appearance occurred four days later, as he came on as an 87th-minute substitute for Étienne Capoue in a 0–0 home draw against Chelsea. On 16 August 2016, Suárez signed for Valencia CF on a season-long loan deal, with an option of a subsequent purchase. He scored his first brace as a senior on 16 October, in a 2–1 success at Sporting de Gijón.
