Messi missed Barcelona’s trip to the United States, where they recorded two wins over Napoli, due to a calf strain.
The 32-year-old might not recover in time for the start of their title defence.
“He’s in the recovery process and I don’t know if he will be ready for the start of La Liga.
“It’s looking difficult,” Valverde told a news conference after a 4-0 win over Napoli in Michigan on Saturday.
Should Messi miss the clash against Athletic, he will look towards the August 25 match against Real Betis to make his season debut.