Arguably, this past week has been the best week of Jimmy Fallon’s career, because not only did he do wonderfully when he took over the Tonight Show from Jay Leno, but he’s been the talk of the Internet, as just about every skit he’s done has gone viral.

So now the folks at the Late Show with David Letterman are starting to sweat a bit, because Fallon is pulling all the top guests and winning the ratings battle between the two shows.

And that’s why Letterman is trying to get Leno on his show as a guest, because if he does, it’ll likely cause viewers to watch in larger numbers, and tune out of Fallon’s show for at least one night.

“There’s been quiet talk behind the scenes for months that Dave will have Jay Leno on as a guest,” said a Daily News source. “[Letterman’s] producers waited until Fallon debuted [on his show], give him space out of respect, but are now ready to pull out all the stops.”

In addition, the source says there’s currently a booking battle going on between the two shows, and producers of the Late Show with David Letterman are keeping an eye on Fallon to see who he’ll book in the future.

“Letterman’s booking department is keeping track of everyone who has appeared on Fallon so far, and considering if they’re worth having,” said the source. “Letterman’s people aren’t taking leftovers.”

Many folks are probably wondering if Fallon will be able to maintain the high ratings he’s received so far, because for one, he’s been able to snag Olympics viewers this past week, plus, a lot of folks are tuning in to him out of sheer curiosity, and they might not do the same in the weeks and months to come.

“The audience will definitely shrink down to a more normal size in a few weeks,” predicted the Daily News source. “Especially after the Olympics are over.”

But we’ll see if that prediction holds true, because there’s a good chance that Fallon’s show will only become more popular.

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