The Portugal international has courted interest from a number of top clubs around Europe, with Manchester United as well as Italian giants AC Milan and Juventus linked with the player.
Veloso's agent, Paulo Barbosa, has revealed Arsenal have added their name to that list after contacting him about the 22-year-old midfielder.
"Actually, we did not have normal contact from the Arsenal board, but from a member of the technical staff at the club," said Barbosa.
"At the moment there is not a formal offer yet, but it is possible that will happen soon as Juventus and AC Milan have shown an equal interest in the player."
A potential stumbling block in the sale of Veloso is the fact he has a contract with Sporting until 2013, although the player claimed earlier this month that he is open to offers to move abroad.
And Barbosa believes Sporting are willing to sell one of the most prized assets if the price is right.
He added: "He (Veloso) is on holiday, now. Sporting Lisbon has not commented just yet, but until a formal offer is made that is perfectly normal.
"As long as there is a good offer for both parties - the club and Veloso - then negotiation can be done for sure.
"It is not secret to anyone that he wants to play abroad."