The Blues are determined to push ahead with their long-term transfer plans.
Previous manager Mauricio Pochettino wanted to keep both players, as they are first team regulars.
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However, The Standard states they will be sold to open up the club's transfer kitty.
Pochettino has officially left the club this week and will be replaced by a younger coach, per British media reports.
One who will make it hard to be sold is Gallagher, as he desperately wants to remain at the club.