The pair both had albeit limited roles with BMW-Sauber and Renault respectively in 2008, but have been excluded altogether from the teams' plans for this year.
Renault has instead plumped for Romain Grosjean, di Grassi's test colleague in 2008, as its third driver, who slots into the loophole allowing some testing for young drivers who have done less than four days of running in the last two years.
Like di Grassi, 24-year-old Asmer also does not qualify for the 'young drivers' in-season test loophole, because he tested five times last year.
"As far as I know BMW-Sauber was very satisfied with the work I did for them last year," a frustrated Asmer told the Dutch magazine Formule 1 Race Report.
"It is clear that the test ban makes it much harder for young drivers," he said.