Kilbane enjoyed a superb two-year spell at The Hawthorns after joining in a £1.25 million move from Preston North End before leaving for double this amount as Albion sought to clear their debts in November 1999.
During his time at The Hawthorns Kilbane, who has never won over the Stadium of Light supporters, established himself as a Republic of Ireland international and The Baggies would be keen take him back, although chairman Clive Stapleton admitted no deal has yet been discussed with The Black Cats.
"We've spoken to lots of agents over four different players," said Stapleton. "We asked a question about Kilbane and we've asked Sunderland to keep us informed.
"But he is not one of the four we're talking about at the moment. I think one of the four will be difficult to do but we're working hard on the other three.
"We are keen to get start recruiting players as soon as possible but it's really very quiet across the whole of the country. Nothing really happens until July."
One of the club's four targets is Ronnie Wallwork and they hope to beat Sunderland to his signature in the next week.
The Premiership new-boys were also linked with an unlikely £3 million move for Fulham defender Zat Knight in the local Birmingham press.
The young defender has impressed in the European Under-21 Championships for England, but it seems unlikely that Fulham would let the young talent leave at this stage of his career.
Meanwhile, Stapleton's attempts to stave off Jeremy Peace's challenge at a club EGM this summer seems unlikely to succeed with the latter stepping up his campaign to be the new Baggies chairman.
"Paul Thompson is a gifted businessman and I'm 99 per cent in agreement with him as to how to run a football club," said Peace.
"But if in his vision of how to run a club there is no place for one of the most talented young managers in the country then I'm afraid his vision is flawed."
