The 18-year-old Scot is currently with Liverpool on their tour of the United States and played for the club in their 1-0 win over Real Betis.
Doak wants to make sure he is playing week in, week out this season and doing that at Liverpool could be a stretch, meaning the club have been considering loaning him out.
There is already interest in the winger in the shape of Leicester City and Southampton.
Both teams won promotion to the Premier League from the Championship last season and could present attractive options for Doak.
Doak is highly rated at Anfield and Liverpool will want to make sure any move is right for him.
Injury stopped a promising season in its tracks for the winger last term and he managed just five senior outings as a result.
Reds boss Arne Slot will be running the rule over Doak in pre-season and it remains to be seen if the door to a possible deal opens for Leicester City or Southampton.
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