We actually broke the news to the Redskins star cornerback about the Dallas Cowboys parting ways with Bryant -- and he seemed a little shocked by the move.

But then ... he quickly started the recruiting process!

"He wouldn't be a bad addition -- hell, come on over!"

"If he can help us win, that's all that matters at the end of the day."

Of course, Norman and Bryant have gone head-to-head a bunch of times over the years -- and formed a true rivalry that got really heated at times.

But Norman is willing to move on in the name of winning.