SUNDERLAND were last night told to improve their initial offer for former Middlesbrough striker Danny Graham after being out-bid by Norwich City in the chase for his signature.

Black Cats boss Martin O'Neill had launched a £4m bid for the Swansea City man yesterday and it was under consideration until the Canaries matched the player's £5m valuation.

Now Sunderland must decide whether to increase their own offer for a player Swansea bought from Watford for £3.5m in the summer of 2011.

The situation is more complicated by the fact Swansea manager Michael Laudrup, who is more than willing to let him go 30 months before the end of his contract, is reluctant to sell until a replacement has been secured.

Former Sunderland striker Kenwyne Jones is the man they want to take Graham’s place at the Liberty Stadium but Stoke City have had an initial offer of £3m knocked back by their Premier League counterparts.

O’Neill is desperate to strengthen his team’s firepower this month and he was quick to make Graham one of his leading targets.

The 27-year-old, born in Gateshead and a boyhood Newcastle fan, has found himself on the periphery of things under Laudrup following the arrival of Spanish hit Michu.

Yet Graham has still grabbed four goals in his last five appearances for Swansea, proving that he is more than capable of finding the net at the top level.

He struck 12 goals in 36 league appearances in his first season in South Wales to help Swansea, under Brendan Rodgers initially, stay clear of relegation trouble.

Reading and Queens Park Rangers have also been interested, while Newcastle have considered making a move only for manager Alan Pardew to rule out a January bid yesterday.

O’Neill is the leading contender to land a striker with North-East roots and the former Middlesbrough front-man is believed to be keen on a return to the region. Norwich, however, would appeal given he is more likely to start most games.

Graham left Middlesbrough, where he had been since leaving Chester-le-Street in 2003, five-and-a-half years ago when he joined Carlisle United. After impressing at Brunton Park he then had two years scoring 38 goals in 91 appearances at Watford following a £350,000 transfer.

Rodgers handed him his Premier League break in June 2011 and now O’Neill has identified him as the ideal man to come in and provide an alternative threat to Steven Fletcher and Stephane Sessegnon.

Provided Sunderland can reach an agreement with Swansea over the sale of Graham, which is looking increasingly likely, then Fraizer Campbell will be allowed to move on.

Campbell, out of contract this summer, is being courted by both Hull City and Cardiff City and he has been told he can leave the Stadium of Light as soon as a replacement is brought in.

Sunderland are not in a position to allow another striker to leave unless they are confident Graham will be part of the squad, although the race is on to have him involved for tomorrow’s trip to Wigan.

O’Neill has already told Louis Saha that he is free to leave and the Frenchman has been in South Africa trying to find a new club to start the final chapter in his career.

Strengthening Sunderland’s attacking ranks is highest in the Sunderland manager’s thinking and he is also looking at other defensive options.

He has already landed 6ft 5in Senegalese international Kader Mangane from Saudi Arabia’s Al-Hilal to compete for a place at the heart of the Black Cats defence.

And O’Neill is keeping tabs on Denmark centre-back Jores Okore, 20, having instructed his scouts to watch him in action for Nordsjaelland. Competition, however, is believed to be strong, with Manchester United, Manchester City and Chelsea among those keen.

* Sunderland are already making plans for the summer and have been confirmed as one of three Premier League teams to play in the Barclays Asia trophy Hong Kong.

Manchester City and Tottenham Hotspur have will join Sunderland and South China for the biennial tournament starting on July 24 and ending on July 29. The tournament will be officiated by Premier League Match Officials and HKFA Match Officials.