The defender is being linked with a summer move to Arsenal.
"It's not a situation I can try to resolve until I know whether I am doing this job (next season)," Monk admitted.
"But for me, Ash should finish his career here, and the club should do all they can to make him a priority.
"Whoever the manager is, Ash should finish his career here because he is an integral part of what this club stands for."
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