The Patriots are very unlikely to sign Cooks to a five year $60 or $70 million contract, which is what it will take to keep him.
He's decent addition while the price is low. They get him for $1.5 million for this year and $8 million and change with the fifth year rookie option in 2018. If they can't work out a deal, the franchise tag for receivers with be over $17 million in 2019.
NE has not chosen to pay skill position players a ton of money, so IMO it would be unlikely that Cooks plays more than two years for the Pats unless he takes a decent sized discount beyond that.
Since Welker left, NE has won two SB's paying their WR / RE / TE about as little as possible. The only receiving threat to get decent money was Gronk, and even he is underpaid given current market pricing.
Paying top dollar for Cooks would not fit their M.O. For the past 17 years, but maybe they will start to pay guys at the going rate.