Former Fulham midfielder Jimmy Bullard will have signing talks with Celtic next week with a view to a season-long loan.
The Tigers want the 31-year-old, who is their record signing, off the wage bill now that they have been relegated from the Premier League in England.
And he could follow Charlie Mulgrew to Celtic Park, with the defender poised to rejoin the club within 48 hours.
Bullard has been linked consistently with the Scottish Premier League runners-up this summer.
English clubs had expressed an interest, but it appears that Celtic have made the most concrete offer.
Jimmy Bullard has got a good touch and fantastic ability, so players like that coming to our club is great for us
And a deal could be done once new manager Lennon has returned from holiday, with Bullard having been given permission to hold talks.
Celtic captain Scott Brown, himself known for his combative midfield play, welcomes the club being linked with big-name players like Bullard.
"He's a world-class player really and he has shown that in the Premier League," he said.
"He has got a good touch and fantastic ability, so players like that coming to our club is great for us."
Bullard, who began his career with Gravesend & Northfleet before spells with West Ham United, Peterborough United and Wigan Athletic, joined Hull from Fulham in January 2009 for £5m.
The Englishman signed a four-and-a-half year contract but picked up a cruciate ligament injury on his debut against West Ham and did not return to action until October.
Bullard missed another two months of the season following a knee injury picked up in December and played just 14 times, scoring four goals, as Hull were relegated to the Championship.
Lennon has yet to make a signing this summer, despite Arsenal defender Sol Campbell, Stoke City winger Liam Lawrence and Cardiff City midfielder Joe Ledley having confirmed that Celtic have expressed an interest in their services.