It appears Town head coach David Wagner hasn’t ruled out a future at the John Smith’s Stadium for the 21-year-old, who cost £300,000 from Carlisle United in July 2015.
But for the time being he is set to remain at Fleetwood, who are sixth in League One, with Charlton 11th.
It is believed the London club offered around £100,000, not nearly enough to tempt Town chairman Dean Hoyle.
Town have a January recall option, but are happy with Dempsey’s progression on the North-West coast.
He has made 22 appearances, and featured in Saturday’s 0-0 FA Cup third-round draw at Bristol City.
Dempsey made 24 Town appearances, half of them starts, last season.
With increased competition (on-loan Manchester City man Aaron Mooy and Croatian Ivan Paurevic were added to existing midfield options Jonathan Hogg, Dean Whitehead and Philip Billing) he didn’t feature in a Town squad this season before his Fleetwood switch late on in the August window.
Paurevic is now set to return to his former club FC Ufa, of the Russian Premier League.
Dempsey is under contract until 2018, when Town can add a further 12 months to the deal.
He is one of two Town players loaned out in League One, with striker Jordy Hiwula at Bradford City.
The former Manchester City player has made 29 appearances, scoring eight times.
The Bantams are fourth in the table.
Meanwhile three Town youngsters have made debuts after being loaned to non-league clubs.
Defender Fraser Horsfall was a starter for Stalybridge Celtic as they beat FC Halifax Town 1-0 in the Conference North.
The 19-year-old had a spell at Northern Premier League Trafford earlier this season.
George Dorrington was between the posts for Ashton United against Whitby Town in the NPL Premier Division.
However an ankle injury meant the 19-year-old former Manchester United player was forced off early om in a game Ashton won 3-1.
Town academy keeper Owen Brooke had a baptism of fire for Radcllffe Borough.
The Lancashire side, who had Town stopper Tadhg Ryan on loan earlier this season, were beaten 5-0 by Farsley Celtic in the NPL First Division North.
The Farsley side featured two former Town players in Aaron Hardy and Lewis Nightingale.
Celtic are managed by another former Town player, Neil Parsley.