Wanderers are reported to have increased their bid for a player who first came to their attention during the club's UEFA Cup campaign two seasons ago.
Bolton failed to land Veloso last January, being unwilling to meet Sporting's valuation.
However, it is suggested they have returned with a £10.2m offer for the club's new regime to consider. Arsenal are also said to be monitoring developments over the player.
Veloso's sale could help balance the books but Sporting are digging in their heels for a higher bid.
Manager Gary Megson has pledged to bide his time this summer before swooping for his targets.
But he could land Portsmouth midfielder Sean Davis before Veloso decides where to play his football next season.
The former Fulham star has reportedly turned down a three-year deal at Fratton Park in favour of a switch to the north west.
West Brom's Paul Robinson is another player said to be on his way to the Reebok Stadium.
Meanwhile, Bolton midfielder Blerim Dzemaili has joined Torino for an undisclosed fee following a loan spell with the Italian side.
The Swiss international, 23, made only one appearance after moving to the Reebok Stadium from FC Zurich in 2007 - a serious injury curtailing his progress.
Bolton have also released Rob Sissons, Nathan Woole and James Sinclair.
Who would you like to see at Bolton? Have your say.
Tweet
