It sounds like there is something configured on the old Mac that may be interfering. OR ... have you been using the new Mac and are now running Migration Assistant after the fact?
How are you transferring, I hope it is not wirelessly, that is very slow usually, and also it presents other possible issues if you are going through a router and its firewall is the issue.
If the Mac is brand new with nothing on it, you may have no choice but to try to quit or cancel the migration. Is that an option? Best would be if there is a cancel button. It should pick up where it left off.
If you have been using the new Mac, I think there also quitting or canceling is the best option at this point, as it appears the transfer won't proceed. If it has been used, could its firewall been set to reject incoming connections?
Last resort would be to force quit or hold the power button. But the migration does not affect the operating system so you should be able to restart ok.
To try again, I recommend making a Time Machine or "clone" type backup of your old machine and use that for migration assistant instead of trying to connect the two Macs. I have done Migration Assistant about 20 times over the years, every time using a backup drive as the place to migrate from, and it has always worked without issue.