Madrid have been looking to bring in a striker after Benzema and Mariano Diaz left this month, leaving Vinicius Junior and Rodrgyo as the club's only senior forwards.
Joselu -- whose full name is Jose Luis Mato Sanmartin -- first signed for Madrid from Celta Vigo in 2009 and scored a career-high 26 goals for reserve team Real Madrid Castilla in 2011-12.
He made one appearance for the first team, scoring in an 8-1 win over Almeria in May 2011, before moving to Hoffenheim in Germany.
Spells at Eintracht Frankfurt, Hannover 96, Stoke City, Deportivo La Coruna and Newcastle United followed before Joselu re-found his goalscoring form at Alaves, scoring 36 LaLiga goals over three seasons between 2019 and 2022.
A move to Espanyol in July last year saw him find the best form of his career, earning a first Spain call-up at the age of 32 in March, during which he scored twice in three minutes in a 3-0 Euro 2024 qualifying win over Norway.