QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
Ilkay Gundogan has commited his future to Borussia Dortmund by signing a new contract.
Barner, 38, has agreed a rolling contract to take over at Fratton Park less than two weeks after he was sacked by League One Crawley.
He replaces Guy Whittingham, who was axed by Pompey two days earlier following a winless run of seven matches which left them 18th in League Two.
Barker said: "This is a fantastic opportunity for me. I'm very excited to be at this club with its great history.
"Everyone knows how passionate the people of Portsmouth are about their football club."
Former Crystal Palace and Brighton boss Coppell, 58, worked in a similar role with Barker at Crawley.
He said: "It's a new challenge for me and I'm very excited. Richie asked if I'd like to be involved and I jumped at the opportunity."