Swansea had an initial offer of £1.5m rejected by the Magpies last week but manager Brendan Rodgers increased the offer, according to BBC Sport.
"We've had a couple of bids that have gone in," said Rodgers, who is hoping to make his fourth summer signing.
"We think he would fit into our style and excite our supporters. We will wait to see if we can agree a deal."
The 26-year-old was loaned to Championship title-winners QPR in January and scored five goals in 20 appearances, playing a significant role in helping Rangers gain promotion to the Premier League.