Some companies do allow employees to roll funds into a 401K. These funds could be from other 401K programs, or they could be from IRAs (Roth and/or traditional). It is up to the rules of the plan. Check the plan description document, or the webpage.
The question is does it make sense to roll funds into a 401K plan?
One benefit of rolling funds into the plan is that all your retirement funds can be in one location. It is easy to track, and easy to rebalance.
In many cases the 401K has higher fees, and in many cases the number of investment choices are limited. Making the IRA funds more flexible and less costly.
These higher costs and limited options mean that many people move funds from their previous employers 401K into IRAs.
There can be one unexpected benefit of rolling funds into a 401K. I worked for a small company, when the total balance of the 401K funds for all employees passed a certain threshold the administrative fees went down for the employers plan. One new employee rolled a ton of money into the plan, this allowed the company to reach a less costly threshold years earlier than they anticipated.