The Patriots will have two high-profile free agents hit the market next week as edge rusher Trey Flowers and left tackle Trent Brown were not franchise tagged. The Patriots typically don’t employ the franchise tag unless they’re close to reaching a long-term extension (e.g. Vince Wilfork 2010, Stephen Gostkowski 2015) or are willing to pay a long term deal with an average yearly salary near the tag value (e.g. Logan Mankins 2011, Wes Welker 2012).
The fact that both Brown and Flowers did not receive the tag suggests the Patriots are not willing to pay top of the market prices for both players.