The former Sporting Lisbon star admits that he is unsure where he will ply his trade next season, but insists he has not been formally approached by Dynamo Kiev
The 26-year-old has been heavily linked with an exit and a move to a new club after impressing for the Seleccao at Euro 2012, which came in stark contrast to his form at the Serie A club during the 2011-12 season.
Dynamo Kiev are known to be interested in Veloso, and the midfielder has dropped a hint that he may not remain at Genoa much longer.
"I do not know anything about Dynamo Kiev," he told reporters. "I really liked my two years at Genoa. I liked playing in Italy, but I do not know if I will stay there.
"The only thing I know about Dynamo is what I read in the press."
Veloso also commented on Portugal's dramatic Euro 2012 quarter-final defeat to Spain in the penalty shoot-out, saying he was disappointed to see the team crash out of the tournament.
"We showed a great balance against Spain," he affirmed. "It was hard to play against them, and harder to accept a defeat like this one.
"We did a great job at the Euros. We are really sad, but we have created a great team."