The Magpies have been chasing the midfielder all summer, but they have so far failed to get a deal over the line.
Newcastle have reportedly already had two offers rejected, with the second of those being worth around £17.5m.
Sampdoria are adamant they will not sell Praet this summer but, according to Sportitalia, Newcastle are ready to bid again.
The Premier League club are now willing to part with close to £20m in the hope that will finally tie up a move for the Belgian.
That amount is over double what Sampdoria paid to sign the 23-year-old last summer from Anderlecht and it could tempt them into selling.