Gotta think any long term deal would be structured like what the 49ers did with Kaepernick, something that looks good on paper but that the team can get out of in a couple years with a minimal cap hit.
Failing that I cant see Gettleman letting even Norman eat up 13 mil of his salary cap on a franchise tag. He's a front seven guy who I think would rather get by with a mid-tier secondary helped by a dominant pass rush.