Yes they can. They can sign him to an offer sheet.
Until Butler signs his RFA, no other team in the league can sign him to anything.
Sure he/his agent can gauge his value with teams he may want to play for, or conversely may be willing to offer him a boatload of cash, but that's pretty much as far as talks can go - nudge, nudge, wink, wink.
Once he does a team can definitely offer to trade for him, possibly as a one year rental (I'm not sure what the tag rules for the following season are in his instance, mostly because of when he was tendered) but more probably on a long term deal - assuming another team wants to surrender a first rounder for him.
And even then NE can match any offer if they so choose.
Sooo, yeah. Until it all plays out NO can't really sign him to fuckall.
And all this is being said with the caveat that he may choose to hold out until well after draft to undermine NE's draft comp (up to the sixth week of the season, I believe?) togain his accrued year, plays under the prorated tag and walks to set his own market.
Which is an whole other can of worms. Altogether.