The Portugal international is among the most highly-rated youngsters in Europe and has previously been linked with a move to Manchester United.
Premier League rivals Arsenal have now contacted Veloso's representative Paulo Barbosa to register an interest in the 22-year-old.
Juventus and Milan are also keen on Veloso, according to Barbosa, although the Rossoneri have previously stated they will not be making a bid this summer.
No formal offer
"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."
Barbosa is confident that, providing the right offer is received, Veloso will secure a move away from Portuguese giants Sporting before the transfer window closes.
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.
No secret
"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."
Reports suggest that Sporting have set a 30million euros (£23.7million) buy-out clause in Veloso's contract, but Barbosa does not believe that will be a major issue.
"The buy-out clause is another issue," Barbosa added. "If they argue that value that would mean the youngsters would never the club."
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