The tennis tournament, which runs from July 27 to August 4, takes place at Roland Garros where Nadal, who will be 38 by then, has won a record 14 French Open singles titles.
Speaking after reaching the Madrid Open quarter-finals -- extending his Madrid Open winning streak to a record-equalling 14 -- Alcaraz said he and Nadal had spoken "a little" about teaming up in Paris.
"If everything goes to plan, like I have already said, we will play the doubles together at the Olympics," said Alcaraz, who turns 21 on the day of the Madrid final on Sunday.
"But there is a long way to go till it gets underway."
Alcaraz, a two-time Grand Slam singles champion, said finding a tournament to warm up for the Olympics together will be difficult.
Not the least of their problems is both have struggled with injuries, Nadal has been hounded by them over the past couple of years and Alcaraz has returned for Madrid after recovering from an arm injury.
"We have said how wonderful it would be to play a tournament before the Olympics," said Alcaraz.
"But that will be difficult.
"On clay the next two tournaments are Rome and Roland Garros, which are hugely important to both of us in terms of the singles.
"Considering we are not at our physical peak it will be tough to play both a tournament and the Olympics."
