Scottish right-back Grimmer, 21, returns to the Town following a seven-game loan spell last season.
Former Manchester United youngster Cole, 22, has been at the Greenhous Meadow since September, having so far scored two goals in 19 appearances.
Both players are scheduled to stay with Shrewsbury until the end of the season.
"Jack's full of power and pace and we have seen the importance of that in this division," said Mellon. "We need to try and get as much of that in the team as possible in the coming weeks."
"Cole's an exciting player. He has that pace, trickery and League One quality we are looking for."
Shrewsbury, 20th in League One, just a point clear of trouble, are also hopeful of bringing back striker Andy Mangan from Tranmere Rovers and have been linked with Northampton Town midfielder Lawson D'Ath.
League One strugglers Shrewsbury Town have re-signed Fulham defender Jack Grimmer on loan and extended the stay of Cottagers midfielder Larnell Cole.