This depends on a number of things, and in some cases would need to move wiring as well. Can you tell us a bit more about your Internet service?
Which modem do you have?
Is it fibre or regular telephone wire?
What speed of service do you have?
If telephone, is there a little dongle where the telephone jack connects to the wall?
Is there more than one telephone jack at the wall plate, and if so, are they labeled?
I Have images of the setup. Don't know if you will find these useful.
A picture is worth a thousand words. Thanks!
Based on this info, I agree with @WestCoasterBC, a move of the router is possible, though not simple. If you want a more centralized location for your wi-fi, an additional access point might be the best option.
Of course you can, it just depends on how much efforts you want to put in or spend to have someone do the re-wiring of tel and cable for you. I am just guessing by looking at the photos that you want to be able to close the utility closet door, right? If that is the case, could some carpentry work achieve the same goal?
For myself.... the installer put the modem in the basement.... but with wireless, I don't care where the modem is.
My Optik TV uses wireless cable boxes. The three TV's can be anywhere in the house where I can find a 120v outlet.
My laptops and other devices run off wifi.