As it stands, the 33-year-old will return to Stoke City next week, but Jewell has claimed that talks between the two clubs have taken place.
"We are hopeful that we will be able to keep Danny. He's come here to play football and he's doing that. He's enjoying it here and I've told him we want him to stay," he told Sky Sports News.
"We're in conversation with Stoke and we will see how things work out but we are certainly hopeful that he will be remaining with us, ideally for the maximum three months."
Ipswich currently occupy 23rd spot in the Championship table.