The Magpies are understood to have tabled a bid worth £25m for Wissa as they look to strengthen an attacking unit that was weakened by the departure of Callum Wilson at the end of last season.
Having failed with previous approaches for Joao Pedro and Liam Delap this summer, Newcastle’s recruitment team have identified Wissa as an attractive target.
The Magpies are confident personal terms would not present any problems to a potential deal, but their first attempt to agree a fee with Brentford officials was unsuccessful.
However, the Newcastle hierarchy are understood to feel there is scope for some negotiating, and are expected to return to the table with a second offer in the next couple of days.
Wissa has returned from Brentford’s pre-season training camp in Portugal to discuss his future with club officials, having been unsettled by the ongoing uncertainty over his future.
Brentford rejected a bid from Nottingham Forest for the 28-year-old earlier this summer, having also rebuffed Forest’s advances when they made an earlier inquiry during the January transfer window.
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The Bees are extremely reluctant to lose Wissa as they have already had to deal with considerable upheaval this summer.
Their manager, Thomas Frank, left to join Tottenham and was replaced by Keith Andrews, another of their forwards, Bryan Mbeumo, recently completed a move to Manchester United, and arguably their most influential central midfielder, Christian Norgaard, has joined Arsenal.
However, there is also likely to be an acceptance that it will be difficult to keep Wissa if his head has been turned and he has decided that his future lies away from the Gtech Community Stadium.
The DR Congo international has a year left on his current contract, but Brentford hold an option to extend the deal by a further 12 months.
Wissa scored 19 Premier League goals last season, and would provide much-needed cover and competition for Alexander Isak if he was to join Newcastle.