Midfielder Jarrett has been offered a three-year contract, Teale and McMillan two years, and Walsh 12 months.
They are attractive terms and all are expected sign up to try their hand in the Premiership.
Jarrett battled back from a broken ankle and badly damaged ligaments to feature in the final few games of the season.
McMillan only forced his way back into the team in the last month, displacing regular left-back Leighton Baines.
Teale was in-and-out during the season and Jewell will be looking for more consistency from the winger if he agrees terms.
Veteran keeper Walsh is expected to be third choice next season, behind John Filan and a summer signing, and will also take up a coaching role.
Three other out-of-contract players, Gareth Whalley, Paul Mitchell and keeper James Salisbury, have been released.
Whalley played a handful of games after joining on a free transfer from Cardiff last autumn, Mitchell spent much of the season on loan at Swindon and Milton Keynes, while Salisbury was an unused substitute in a couple of matches at the start of the campaign.
The retained list was one of Jewell's many jobs yesterday when he returned to work after the club break in Barbados.
His search for new additions to the coaching and backroom staff continues, and he has reiterated his desire to bring in someone to help negotiate transfers and contracts but has stressed that person won't hold the title of director of football or general manager.
Jewell told the Evening Post today: "Dealing with new signings and agents is a time consuming business and I don't want to be distracted from the training field and getting the players ready for the season.
"The person I appoint will deal with the mechanics of the transfer market after I have selected the player I want to sign.
"I have heard the phrase director of football and general manager being bandied about but these titles can be misleading.
"The new role will be specifically to assist me in completing transfers and other football administration duties.
"This won't be the only appointment I make as the Premiership has huge demands and I will be recruiting people to meet those needs."
John Benson's name was linked with the role but I understand the former Latics manager, now at Birmingham City, will not be making a return.