Liverpool boss Brendan Rodgers says Raheem Sterling "is being led by his representative" as he seeks a move.
Aston Villa manager Tim Sherwood has revealed in-demand defender Ron Vlaar has told him he wants to stay at the club.
The Tigers were unsuccessful with a bid for the 25-year-old Englishman, reported to be in the region of £4.5million, last month.
However, Bruce will not renew his interest in the former Scunthorpe striker who reportedly cost the Scottish champions £2.4million in 2010, and who has also been linked with QPR and Norwich.
"We had a bid for him rejected and I can't see there being any change in that," Bruce told BBC Radio Humberside.
"We've got other irons in the fire and we hope that we can get one or two strikers in before the start of the season.
"It's obvious that we struggled to score goals last season so that has got to be the aim for us.
"We've still got six weeks before the season starts and we're actively looking."