Klose, who turns 33 on Thursday, is set to part company with Bayern Munich, where his contract expires at the end of the month, and will announce his switch from the Bundesliga to the Spanish league.
The Germany star, who has scored 61 goals in 109 international appearances, has rejected Bayern's offer of a one-year contract with the option of an extra year having spent most of last season on the bench.
Bild report Klose wanted a two-year deal and was demanding a higher salary than Bayern were prepared to offer him.
Competition is fierce for places up front at Bayern with Germany striker Mario Gomez netting 28 league goals in 32 matches last season.
Croatia striker Ivica Olic and new-signing Nils Petersen will also be competing for starting places next season in Munich's attack.
Klose has been at Bayern since 2007 and a host of clubs including Italy's Lazio and Premier League side Everton are reported to have also been interested in signing him.
In four years, Klose has scored 53 goals in 150 games for Bayern and is closing in on Gerd Mueller's all-time record of 68 goals for Germany.
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