The Sunday Sun says Simpson has still not signed the five-year contract mentioned back in May.
Pardew gave a ringing endorsement of the right-back to owner Mike Ashley - saying he believes the former Manchester United man can play for England.
That was understood to have swayed the issue in Simpson's favour.
However, no deal has been done yet and Alex McLeish - a long-term admirer - is keen to take him to Aston Villa if Newcastle are willing to sell. Villa need a right-back after England man Kyle Walker went back to Spurs.