Hodgson's contract runs out at the end of the season and talks to sign a new deal have not yet begun.
The former Liverpool boss led the Baggies to their highest ever finish in the Premier Legaue last season and a record-breaking third consecutive campaign in the top flight looks likely with West Brom currently 13th in the league.
Morrison told The Daily Mail: "It is very important to look at what he has done for the club. He has got midtable finishes whereas previous years we have been going down.
"Everyone looks at this club as a solid Premier League team so it is important they tie him down."
Although the former Middlesbrough man wants Hodgson to remain at the Hawthorns, he understands that the manager's fine work in the west Midlands will make him a leading candidate for the national job.
"Roy is on the pitch every day, coaching, telling you where to be on the pitch. It has given everyone that self-confidence and I can see why England may want him," he stated.