The double world champion is due to return to Formula One with Renault next season after two years away from Grand Prix racing.
The Monaco Grand Prix and double Le Mans 24 Hours winner is racing at Indianapolis on Aug. 23 with Arrow McLaren in a bid to become only the second driver to win the so-called Triple Crown of Motorsport.
This year is likely to be Alonso's last appearance at Indianapolis for at least two years, with Abiteboul emphasising that the 39-year-old would not be allowed to race there while contracted to Renault in F1.
Asked if Alonso might do so if there was no calendar clash, with the Monaco Grand Prix and Indianapolis usually on the same May weekend but the latter race postponed this year due to the COVID-19 pandemic, the reply was the same.
"The straightforward answer is that actually I'm hardly breathing until next weekend, that he is stepping out of his racing car in Indianapolis," the Frenchman told reporters in a Spanish Grand Prix video conference.
"But I can be very clear that once he's with us, that's for good, and for a while. So no distractions."
Alonso was unhurt when he began practice for his third attempt at Indianapolis on Thursday. The race is due to take place behind closed doors due to the pandemic.
The Spaniard led the Indy 500 for 27 laps on his 2017 debut before his car's engine expired. He failed to qualify in 2019. (Reporting by Alan Baldwin; Editing by Ken Ferris)