If, as reported, he received the "non-exclusive franchise tender", he most certainly CAN negotiate with other teams. Generally this option is not used and mostly with the intent of working a trade.
From Wiki:
"There are two types of franchise tag designations: the exclusive rights franchise tag, and non-exclusive rights franchise tag:
An "exclusive" franchise player must be offered a one-year contract for an amount no less than the average of the top five salaries at the player's position as of a date in April of the current year in which the tag will apply, or 120 percent of the player's previous year's salary, whichever is greater. Exclusive franchise players cannot negotiate with other teams.
A "non-exclusive" franchise player must be offered a one-year contract for an amount no less than the average of the top five salaries at the player's position in the previous year, or 120 percent of the player's previous year's salary, whichever is greater. A non-exclusive franchise player may negotiate with other NFL teams, but if he signs an offer sheet from another team, the original team has a right to match the terms of that offer, or if it does not match the offer and thus loses the player, is entitled to receive two first-round draft picks as compensation.
It is the team's choice whether it uses an exclusive or a non-exclusive franchise tag. While it may seem that a team would always choose the exclusive option, there are two reasons a team might prefer the non-exclusive option instead. The first is that the salary is based on the top 5 salaries of the previous year instead of the current year, which could be a significant difference. The second reason is that a team may want the opportunity for the two first-round draft picks they would receive if they lost their player."
