The midfielder could be sold this summer by the Blues as they seek to ease Financial Fair Play concerns.
Gallagher has less than 18 months to run on his existing deal, so his future must be decided this summer if Chelsea are to avoid losing him for nothing next year.
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However, the London Evening Standard says Gallagher will not be rushed into a decision by management.
Gallagher wants to avoid any distractions as he pushes to make England's Euros squad this summer.