The couple attended the Gaucho International Polo game, billed as being the "ultimate celebration of Argentina's sporting and cultural heritage".
Watching in a private box with friends, Price and Penna appeared to become aware of the photographers, before both took turns to take pictures themselves.
Despite former glamour model Price stating that she is not dating the Argentinian model, Penna was seen with his arm around her and kissing her on the cheek.
Writing afterwards on Twitter, Price said: "Enjoyed the Polo tonight! England WON wooo (sic)."
Earlier this week, the mother-of-three was granted a divorce from second husband Alex Reid, whom she split from last year.
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