It is believed that Phillips has been offered a two and a half year deal with a further option on top of that.
Phillips is hoping that he can sort out a pay-off with Rovers with the remaining six months of his contract as the Pirates are the ones who have said he can leave the Memorial Ground.
In the last week Phillips agent has been touting his name but it now seems that Crewe are firm favorites to seal a deal with the keeper.
Phillips told the official club site "I am very pleased with the length of the contract because I will have to move away from Bristol for the first time. I don't want to uproot my family and then have to do it again in 6 or 12 months, so the security of two and half years is attractive. It also shows that Dario has faith in me.
"It has been a struggle being away from my family for four months, especially as we have a newborn but needs must and I have been on loan at Shrewsbury and now Crewe.
"I have spoken to my wife about the possibility of moving to Cheshire and she understands that in football you are never in one place for too long. I have been lucky really because most of my career has been based in Bristol where my family and her family are.