The Owls boss has made the international striker his main target after Patrick Kluivert turned down the chance to have a trial at Hillsborough.
Chairman Dave Allen revealed that Wednesday were chasing the £2million player and admitted a bid had been made for the former Derby and Spurs man during a pres conference last week.
But no move is certain yet as Rasiak still has not spoken to The Owls, at least Laws is making progress with his negotiations with The Saints.
He told the Yorkshire Post: "We are hoping to make some kind of breakthrough in the next dew days, until we get permission to talk to the player, there is no other issue to be discussed.
"Southampton have been in touch. It's a positive note, they are not telling us to go away. I know it has been a long drawn-out process, but the fact that it got out in the open has made it more difficult because everyone is impatient."
Goals from David McLements, Sean McAllister and Richard Wood's younger brother, Todd, sealed a 3-2 win for Wednesday over Sheffield FC last night.
The game, part of Sheffield's 150th anniversary celebrations, saw a youthful Owls side turn out although Yoann Folly, Burton O'Brien, Rocky Lekaj and Mark Beevers played their part.