You can ask him, but don't expect the police to be helping that fast.
According to Texas property code 24.005, you must provide 3 day's written notice once the person is overstaying. I don't think you can immediately consider them to be overstaying if they're paying rent, though. If they can be considered a month-to-month tenancy, then you must give them one month's notice under Texas property code 91.001, unless you have a specific reason (like they were convicted of using the property for prostitution) that allows you to only give 10 day's notice. Only if they stay beyond that month's notice period would you be able to give the 3 day's notice. After the 3 days have passed and they are still on the property, you can file an eviction lawsuit.
According to the Texas Rules of Civil Procedure, rule 510.4, the date of the trial must be at least 10 days after the lawsuit is filed (but no more than 21 days.) You don't pick the date; your local court dockets the trial. Let's assume they docket the trial for the minimum of 10 days out, the trial finishes on the same day it starts, and you get a judgement in your favor, and let's assume the person doesn't file an appeal.
According to Texas property code 24.0061, a writ of possession may not be issued before the sixth day after the date on which the judgment for possession is rendered unless certain conditions are met. And once the writ is executed, a minimum of 24 hour's notice is given by the police that the person really really has to leave. After that, the police will actually remove them.
So, overall, it's going to be a minimum of 3+10+6+1 = 20 days between when you first give them written notice and when the police will kick them out, and I would be surprised if you could actually do it that fast. If you need to give a month's notice first, then even if that month is February it becomes at least 48 days.