Sonntagsblick said the 24-year-old Swiss is this week in Brazil, where he is competing in Felipe Massa's annual Florianopolis kart race.
"Before that," said veteran correspondent Roger Benoit, "Buemi will again be signed as reserve driver for Red Bull and Toro Rosso.
"Team advisor Helmut Marko has agreed the renewal with Buemi," he added.
Meanwhile, the Belgian newspaper Le Vif reported that Jerome d'Ambrosio is likely to remain Lotus' official third driver in 2013.
The 27-year-old, who is managed by Lotus team boss Eric Boullier's Gravity stable, has been working to return to the grid.
"My management is working hard," said d'Ambrosio, "but it's difficult because there are many experienced drivers without teams. We'll see."