Gallowgate-born Snodgrass was coveted by Celtic as a youngster back in 2003 but chose to move to Livingston for a more realistic chance of first team football.
His career since has taken him to some big clubs such as Leeds United, West Ham and Aston Villa.
But the Scotland international failed to establish himself at West Ham after a big £10 million move in January 2017.
He was sent on loan to Villa last summer and has been a key player in the club's promotion bid, which will be decided either way in Saturday's Championship Play-Off final against Fulham.
It has been all change at West Ham with Manuel Pellegrini appointed manager as the Hammers plan to go for it in the transfer market by handing the Chilean a £75 million warchest, as reported by the likes of The Mirror.
That kitty will also reportedly be boosted further still by a raft of sales with Snodgrass one of the East London club's most saleable assets.
And Celtic could snap up the 30-year-old for a relative bargain between £5-6 million to fend off a renewed challenge from Steven Gerrard's Rangers.
He would add goals, assists and workrate to the Hoops, who will be looking to protect the dynasty Rodgers is creating at Celtic Park.