The deal for the services of the former Palace and Birmingham man expires in June 2010 but Morrison, who is rumoured to be the biggest wage earner in the club, has suggested that he is to be offered a longer term deal.
"The manager has said he will have a word with me about it but I am just enjoying it and if I get 15 or 16 goals this season I would have said that this is a good season considering it is my first at Coventry and hopefully, I can keep going," he said to the CT.
"I have got eleven goals and there is another nine games to go. I should have had a hat-trick on Saturday so I should be on thirteen but if I get a few more chances like I did at Preston I will try to put them away.
"I am enjoying my football here and I am glad I made the move here. The club has great supporters and a great manager who has got faith in me so I am very happy here."