The 30-year-old midfielder was the subject of a loan enquiry from Scottish giants Celtic on transfer deadline day.
Bhoys boss Brendan Rodgers identified that Morrison was down the pecking order at Albion and asked to have the player on loan but the Baggies turned down the request.
Having only learned late on that the Glasgow powerhouse were keen, Morrison is aware now that if he continues to be cast aside by West Brom, then he could be off to Parkhead in January.
"It was just an enquiry, that's all," said the Scotland international.
"Obviously I am not playing at my club at the moment and there was an enquiry. But the club said no.
"With my position at the minute I would definitely have considered it. But it didn't happen so I am just looking forward to trying to get back into the team.
"The last day of the window was the first time I'd heard of it. My first goal is to get back playing regularly for my club again and try and force my way back into the Scotland team.
"January is a long time away, but I'd have to seriously consider my position at the club if I'm not playing. I was injured for a bit and I'm still not getting games. I'll have to look at it.
"It's hard for the management at the club to throw me back in when I haven't played for so long. They're under pressure as well. I'll keep trying to get fit, wait for my chance and take it when it comes."