When asked about the speculation, two-time world champion and former McLaren driver Fittipaldi said: "The first thing I want to say is that Alonso is a master.
"He is the master of formula one today and should win more titles.
"He could go anywhere and look good, but I think Ferrari has the potential, the ability, the necessary resources to give him the car he finally deserves next year," the Brazilian added.
Asked again if Alonso should stay at Ferrari in 2015, 67-year-old Fittipaldi insisted: "If you ask me, I think it's clear what Alonso should do -- stay at Ferrari.
"Fernando must stay another year."
Fittipaldi said he enjoyed the long wheel-to-wheel battle between Alonso and reigning world champion Sebastian Vettel during the British grand prix.
"It was absolutely brilliant," he told Spain's AS sports newspaper. "Vettel the good driver, and Alonso the maestro."