Pochettino has seen his side slip outside of the top four and is ready to bring in reinforcements when the transfer window opens next week.
He is ready to battle Chelsea for England midfielder Barkley, who is returning to fitness after having surgery on a ruptured hamstring.
Barkley, out of contract in the summer, played in a behind-closed-doors game at Everton’s Finch Farm training ground early last week.
And the 24-year-old, who appears on the wanted list of Arsenal and West Ham as well as the Blues, will be ready for first-team action in time for the transfer window.
Manchester United left-back Shaw is another long-term Pochettino target and has struggled to settle at Old Trafford since his £30million move from Southampton in 2014 – he is also interesting Newcastle.
Jose Mourinho will let Shaw leave the club to finance a £25m move for Fulham’s Ryan Sessegnon.