Cavani is in his third season with Paris Saint-Germain and has 17 goals in 39 matches across all competitions for the runaway Ligue 1 leaders this term.
However, the 29-year-old customarily features in a wide attacking role for Laurent Blanc's side to accommodate talisman Zlatan Ibrahimovic at centre-forward.
Fossati, who led his country to third place in the 2004 Copa America, believes Uruguay's hopes at the 2018 World Cup would be bolstered considerably by Cavani operating in the central striking role he filled with such distinction at Napoli.
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As City prepare to welcome Pep Guardiola as head coach for 2016-17, with an overhaul of their playing staff expected to accompany his arrival, Fossati believes Manchester could be Cavani's ideal destination.
"Cavani needs to play as a centre forward," Fossati, now boss of Qatari side Al Rayyan, told www.sc.qa.
"He is being used as a winger by PSG and also sometimes as a midfielder. I can understand this is because Zlatan Ibrahimovic plays as a centre forward.
"Guardiola normally employs two or three forwards and therefore I would strongly advise Cavani to join them next year."
Fossati recalled an experience from his time as Uruguay boss to outline the possible benefits of a City switch for Cavani.
"I remember I benched Diego Forlan when I was national team manager," he added. "He was getting very little playing time at Manchester United then.
"When he moved to Villarreal the national team partied because we knew that he will get valuable match time, which would also benefit us."