The news was revealed by the Spanish teenager's teammate for the forthcoming Hungarian grand prix, Sebastien Buemi, even though the Red Bull sister team is yet to confirm officially that Sebastien Bourdais has been ousted.
It is believed Alguersuari's straight-line aerodynamic test, which is the only kind of non-grand prix running allowed within the 2009 season, will take place at a circuit in Italy.
On a visit to a Swiss kart track this week, 20-year-old Buemi said the revised STR4 will bring Toro Rosso in line with the specification of Red Bull Racing's RB5 car at the recent British grand prix.
"We should then have the potential to qualify between positions eight and 12 and our objective will be to gain points," he told the Swiss press.
Buemi said the fact Bourdais has been ousted has not shaken him.
"F1 is the highest championship in the world. Even if you have been successful in other categories, it is not easy to arrive in F1 and do the same," he insisted.
"Everyone has his problems," Buemi added. "We have a good relationship but I have to concentrate on my work. Everything else I try to ignore a little bit."