He had done a limited number on Monday before having to abandon due to rain.
Yamaha said the nine times world champion had ended Tuesday with "an improved feeling and a more positive impression compared to yesterday."
The rider's father Graziano told Italy's RAI radio that he was optimistic.
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"Should he ride? As his father, I'd say no. As Graziano, as a friend, I'd say yes."
Rossi suffered the break in an accident while riding an off-road enduro bike on Aug. 31.
He missed the San Marino Grand Prix at Misano and Yamaha said last week that Dutch Superbike rider Michael van der Mark would replace him for the race at the Motorland Aragon circuit on Sept 24.
The Italian is fourth overall and 42 points adrift of Honda’s Marc Marquez and Ducati’s Andrea Dovizioso, who are tied at the top of the championship with five races remaining.
Yamaha team boss Lin Jarvis said last week he doubted Rossi would go to Spain unless he felt he could be fighting for the top five or six positions.
In 2010, it took Rossi six weeks before returning after he broke his right leg in practice for the Italian Grand Prix. This time, doctors had recommended a recovery period of 30-40 days.
(Reporting by Alan Baldwin in London, editing by Toby Davis)
