Mulgrew began talks over a new contract quickly after Brendan Rodgers was appointed manager in late May but the situation was not resolved before Celtic set off for a training camp that will see them play four friendlies.
When asked about Mulgrew, assistant manager Chris Davies told STV: “There’s no update on that. That one is ongoing. We are happy with the players we have got in here and we are working towards the future.”
Central defenders Dedryck Boyata and Jozo Simunovic remain out through injury ahead of Celtic’s opening Champions League qualifier against either Lincoln Red Imps or Flora Tallinn on July 12 or 13, but Celtic are not rushing to add to their back four.
“It’s not a concern,” Davies said. “We have got players that can play in that area, we have got players that can cover in that area. It’s a bit unfortunate Simunovic and Boyata are injured at the moment but we’ve got players in that position.”
Despite being in no rush to add to his squad, Rodgers has pinpointed new signings.
“There is a lot of work being done by the club and the recruitment department,” Davies said. “Everything is ongoing. These things take time, so we’ll see how we go in the next few weeks.
“We have got our targets and have identified what areas we need to strengthen.”