The 34-year-old died from internal injuries after being hit by a pick-up vehicle that mounted a central reservation in Wallasey on Monday.
The married father-of-two had been trying to stop a Mitsubishi Challenger, which was driven from an estate agents in Birkenhead.
The men aged 18 and 30 are in custody.
Officers have also executed warrants to carry out searches at four properties in the Oxton and Wallasey areas as part of the investigation.
A mid-terrace house in Wheatland Lane, Wallasey, just yards from where the pick-up was found, was among those searched.
PC Phillips had been responding to reports of a burglary in Woodchurch Road, Birkenhead.
He and a colleague had been attempting to stop the vehicle using a tyre-puncturing "stinger" device at 02:10 BST.
Fellow officers tried to save his life before he was rushed to hospital, but he died shortly after arrival.
The red pick-up vehicle was found abandoned in Corbyn Street, Wallasey at 02:55.
Det Ch Supt Paul Richardson appealed for anyone with information to contact the force.
Sir Peter Fahy, chief constable of neighbouring force Greater Manchester Police which lost PCs Nicola Hughes and Fiona Bone in a grenade attack three years ago, said: "Every time an officer is killed in this country it brings back memories of Fiona and Nicola."
He added that PC Phillips's death, "not only shows the dangers officers face day in and day out but it shows if we want a routinely unarmed police force, that uses the minimum of force, that's a sacrifice officers carry and it's important the country recognises that and takes it seriously."
Merseyside Police Federation has set up a memorial fund in tribute to PC Phillips for his wife Jen and daughters Abigail, seven, and Sophie, three, which has raised more than Â£30,000.
Another fundraising page has been set up by Nicola Goode who used to work with PC Phillips' wife.
Two men have been arrested on suspicion of murdering PC Dave Phillips who was struck by a car and killed during a pursuit in Merseyside.