Manchester United's director of football Jason Wilcox is a significant admirer of Hall and has been pushing the club to pursue a deal, according to multiple reports.
The move forms part of a broader defensive rebuild at Old Trafford, where a long-term successor to Luke Shaw is considered a priority alongside two central midfielders and a senior striker.
The club is already reported to be close to signing Atalanta midfielder Éderson as the first piece of that puzzle.
Hall joined Newcastle United on loan from Chelsea three years ago before the move was made permanent. He has since developed into one of England's most promising young full-backs, admired for his range of passing and ability to drift infield into central positions.
His situation at St James' Park has become more complicated in recent months. He found himself behind Dan Burn in manager Eddie Howe's selection for key fixtures late in the season, and was omitted from Thomas Tuchel's England squad for the World Cup.
The combination of a difficult relationship with his manager and the tournament snub has raised questions about whether he may be open to a fresh start.
Newcastle finished twelfth in the Premier League last season — their worst campaign in several years — which may make it harder to hold on to players with ambitions at the highest level.
United have also been linked with other left-back options including Eintracht Frankfurt's Nathaniel Brown and West Ham United's El Hadji Malick Diouf, suggesting they are assessing several candidates before committing.