The Italian midfielder left Parkhead seven years ago.
Donati argues with former Rangers man Gennaro Gattuso
Donati spent just two-and-a-bit seasons at Celtic under Gordon Strachan and - very briefly - Tony Mowbray, but despite his fleeting visit, the midfielder retains fond feelings for his former side.
And though 35, Donati, who plays for Italian Serie B Bari, believes he could still do a job for the Bhoys.
Donati (C) in action for Bari
"I think he should sign me!" Donati jokingly told the Scottish Sun when discussing the Northern Irishman's appointment.
"I look out for all Celtic’s results and follow all every bit of news about the club. They are a team very close to my heart.
"For that reason I’ve got them tattooed on my chest. I love the club colours, the fans and the life in Glasgow. I miss it a lot."
Donati, signed by AC Milan as a 20-year-old, went on to become a league winner at Parkhead in 2008 and lifted the Scottish League Cup the following spring.
Donati (R) in his AC Milan days
He was part of a Celtic side that reached the last 16 of the Champions League in his debut season and appeared in both legs of the Bhoys' 4-2 aggregate defeat to Barcelona.
However, in late August 2009, having appeared 12 times in little over a full season, the former Italy Under-21 international returned home with Bari, and played for both Palermo and Verona before rejoining the Puglia side for a second term in 2014.
Donati (R) celebrates Celtic's 2009 League Cup success