Should Bolton be given permission to talk to the player they are convinced they will be able to bring him to the Reebok Stadium before the end of the month.
Should they be successful the deal would represent a massive coup for Bolton who, after a difficult start to the season, have shown improving form of late.
However, signing Veloso would still represent a remarkable move and would eclipse even their audacious signing of Nicolas Anelka.
Sporting have suggested they would only part with one of their best players for a fee in the region of £20 million, though Bolton believe that, should they structure a deal to allow for Sporting to benefit from any sell-on profit then the cash up front figure could be drastically reduced.
Veloso is a regular in the Portuguese national team and one of the most highly rated of the current crop of youngsters coming through the ranks.