Karim-Richards is a 29-year-old former Sheffield United striker who joined Celtic on transfer deadline day.
Leigh Griffiths is 25 years of age and is the best striker on the books of the Scottish Premiership giants at the moment.
Former Celtic manager Hay believes that the duo will be able to play together just fine.
“Kazim-Richards looks, at first glance, to be the ideal foil for Leigh Griffiths,” the former Celtic midfielder wrote in The Glasgow Evening Times. “You cannot expect Griffiths to maintain his form all year, he needs a strike partner.
“Nadir Ciftci went out on loan but a big part of his issue was there was no game time. We don’t know if it would have been any different if he had featured regularly, but if you are not playing then you are not going to be match fit.
“There are two strikers there now and it seems logical to try the two together and give them the opportunity to establish some kind of partnership.”
Erik Sviatchenko also moved to the Bhoys in the January transfer, joining Ronny Deila’s side from FC Midtjylland.
Hay has suggested that he has been impressed with the 24-year-old Denmark international defender.
“The Dane, Sviatchenko, also looked promising when we have seen him, especially given that he has just been thrown in,” wrote the former Scotland international.
“It is unfortunate Jozo Simunovic picked up another injury, which has meant the two have not had a chance to strike up an early partnership together as that is the long-term intention.”
Celtic are at the top of the Scottish Premiership table at the moment with 55 points from 24 matches.
The Hoops are three points clear of second-placed Aberdeen, who won against them at home in midweek.
The Glasgow giants have the strongest squad in the Scottish Premiership, but they appear to be struggling at the moment.
Hopefully for the Celtic fans, the new signings will make a difference for the team between now and the end of the season.