WEST HAM UNITED have told Sunderland to name their price for Jermain Defoe – but the Black Cats are adamant they will not be selling their leading goalscorer no matter what they are offered before the transfer window closes.

Sunderland officials rejected West Ham’s improved £6m offer for Defoe yesterday lunchtime, but that has not deterred the Hammers hierarchy from maintaining their interest in the 34-year-old.

Slaven Bilic identified Defoe as his leading target long before the transfer window opened, and while the West Ham boss has also been linked with Brentford’s Scott Hogan, he has instructed those working above him to continue pushing for the Sunderland striker.

Black Cats chief executive Martin Bain expects to receive a third approach shortly, and sources in London claim West Ham are keen to convey the message that money is no object as they look to safeguard their Premier League status in their first season in the former Olympic Stadium.

Sunderland did not pay a fee when they signed Defoe from MLS side Toronto FC in January 2015 as they effectively swapped the striker for Jozy Altidore, and they could lose him for next to nothing in the summer if they are relegated as there is a clause in his contract enabling him to leave Wearside in the event of his current employers dropping into the second tier.

Financially, it is possible to construct an argument for selling a player who will be 36 by the time his current contract is due to expire in 2019. However, there is a shared acknowledgment among Bain and David Moyes that selling Defoe at any price does not make footballing sense with the Black Cats stranded in the relegation zone, just two points off the foot of the table.

When he was asked about a possible bid for Defoe on Christmas Eve, Moyes described the striker as “priceless” and “indispensable”.

Only Diego Costa, Zlatan Ibrahimovich and Alexis Sanchez have scored more than Defoe’s 11 Premier League goals this season, and the former England international is responsible for 58 per cent of Sunderland’s goals in the top-flight.

He has scored 30 goals in 70 Premier League appearances since moving to the Stadium of Light, and Moyes long ago concluded that it would be impossible to replace him if he was to leave this month.

Last summer, Sunderland rejected Everton’s £25m offer for Lamine Kone because Moyes did not think he could replace the centre-half, and it would be even more difficult to plug the gap Defoe would leave if he was to return to London before the end of the month.

With Sunderland saddled with debts of more than £140m, Moyes would not be guaranteed to receive the whole of any transfer fee in order to source a replacement, and even if he found himself with £8m-or-so to spend, it would be impossible to recruit a proven Premier League goalscorer for that price.

The unknown factor in the current impasse is Sunderland owner Ellis Short, as the Irish-American businessman will ultimately have the final say over all transfer matters.

However, while Short is reluctant to run up any more debts until he is able to sell at least some of his stake in the club, he will not be putting Moyes under any pressure to raise funds.

With a place in the Premier League now worth a guaranteed £100m-a-season, the cost of relegation far outweighs the potential profit involved in selling Defoe. Like his manager, Short will surely be aware that Defoe’s presence in the starting XI represents Sunderland’s best chance of clambering out of the bottom three before the end of the campaign.

The situation might change if Defoe was to openly agitate for a move, but while the Londoner retains a strong affinity for West Ham, where he started his senior career, he has also formed a powerful attachment to Sunderland.

Only last week, he told Sky Sports: “There’s going to be speculation because, let’s be honest, the people that score goals are wanted.

“Over the years, anyone that has scored goals has been talked about in terms of moving to different clubs. I think it’s just part and parcel.

“The players don’t really get involved – you just get your head down and you play football. It’s a good feeling to be wanted, but when you’re playing well and scoring goals, then you must be enjoying being at the place you’re at.”

Meanwhile, Seb Larsson is also attracting interest from elsewhere, with Italian side Fiorentina pondering the offer of a two-year deal.

Larsson, who recently returned to action following summer knee surgery, is due to become a free agent at the end of the season, and Fiorentina are hoping to push through a cut-price switch.

Three or four weeks ago, it looked as though Larsson’s first-team prospects on Wearside would be limited, but with Lee Cattermole, Paddy McNair, Duncan Watmore and Lynden Gooch all facing long-term lay-offs, and Didier Ndong set to miss the next month on international duty at the Africa Cup of Nations, the Swede has become a key member of Moyes’ first-team squad.