Both players are held in high regard at Old Trafford, but they are also very well known by Fulham boss Rene Meulensteen from his time with United.
Now Fulham have now made a move for the midfield pair and hope to conclude deals for both players by Friday.
Tunnicliffe has just returned to United following an impressive loan spell at Championship side Ipswich Town.
The 21-year-old has made two league cup appearances for United, but has never featured for them in the Premier League.
Cole, like Tunnicliffe, has never featured for United in the league but the 20-year-old has played in the League Cup.