According to The Sunday Mirror, Albiol, who is rated at around £10 million in the transfer market, could help strengthen the weak point in the Arsenal side - the defence - that contributed to the club's problems during the latter stages of the season, resulting in a campaign that had promised much ultimately yielding no silverware.
Albiol is thought to fit manager Arsene Wenger's blueprint for the Gunners of emerging young talents who can develop alongside the likes of Cesc Fabregas and Robin van Persie at the Emirates.
The 22-year-old is a product of Valencia's youth system and has even captained Los Che on several occasions. His performances for the club - in defence as well as defensive midfield - have earned him high praise and two caps for the Spanish national team.
It is thought the only thing that has held the youngster back from playing more times for his country is the miserable season endured by his club this season, in which they barely avoided relegation and were knocked out of the Champions League in the group stages.
They did, however, win the Copa del Rey, and Albiol was a major player in their strong rearguard that saw them overcome Barcelona on the way to beating Getafe in the final.
Blues linked with Zlatan
Messi wants Ronaldinho stay
Palermo reject Gunners link
Voro Seeks Focus