Owls chief executive Kavan Walker has confirmed that an offer for around the £100,000 mark for Scottish international Ross has been put to the SPL champions, who are currently touring North America.
Ross is a 24-year-old who has also been linked with a move to Premiership newboys Wigan Athletic despite Wednesday's offer being accepted by The Gers.
Coughlan has been linked all summer long and after Bristol City tabled a bid around the £50,000 mark, Paul Sturrock also had to move in.
The experienced Dublin-born defender was captain of the Plymouth team who won promotion in back-to-back seasons under Sturrock.
The Owls have also been linked with a move to sign Tranmere's Canadian star Iain Hume and Paul Murray of Portuguese side Beira Mar.