Albion signed the 20-year-old striker on loan from Manchester City last summer, and have seen him make a huge impact at The Hawthorns, where he has scored 10 goals so far.
Albion have an agreement in place to sign Miller from City for a set fee - but only have until the end of January to take up the option.
Mowbray knows Miller's valuation could go through the roof if he continues his rich vein of form, and he said: "It's not about whether we want to pick it up or not. Everything is put in place but the player has got to be happy.
"That's the final piece of the jigsaw. Because Ishmael has done so well he will be looking at potentially wanting to keep his options open.
"He has got to make some decisions along the line - is he happy here? Does he think this is the right type of club for him? Do we play the football that helps his game?
"I would hope he does enjoy it here and thinks it's the right place for this stage in his career and hopefully something will be sorted out."
Mowbray added in the Express and Star: "To get him at a certain price we would have to get him signed up this month.
"If we don't do that he is not going anywhere. He is staying here and hopefully scoring goals.
"After that the price goes to whatever Manchester City want to ask.
"He might score another 30 goals before the end of the season and then they would have a £10million strikers on their hands."