My company offered to cover up to $20,000 of my moving expenses. They said it would come out of my paycheck. I assumed they would gross up to cover all costs. However - here's the catch. Grossing up means then need to pay me $27,000 to reach the $14,000 I actually spent (which is over their budget).

They've since offered to pay me the full $14,000 in my paycheck without taxing it, but then I'm assuming I just get hit with the taxes later.

My company has not done this before and therefore I need to understand what my possible options are.

If I take the $14,000 how much should I expect to pay later in taxes? How can I figure this out?
Thanks!

The $14,000 will be taxable. Claim the allowable expenses on Form 3903.