The batsman made his return from a knee injury this weekend as Surrey took on Yorkshire at Headingley in the LV= County Championship but a combination of Vikram Solanki's decision to bowl and rain meant the 32-year-old did not get the opportunity to bat until Sunday morning.
Morris is convinced, however, that there is enough cricket to be played between now and the opener at Trent Bridge to get Pietersen fully up to speed for the summer's main event. And he told BBC Radio Five's Sportsweek programme: "It's very encouraging that Kevin is back playing again."
He added: "I know he's worked very hard in practice on preparation and on his fitness. He looks very fit.
"Clearly it's important that he gets some cricket under his belt before the selectors actually sit down and pick the first Ashes squad.
"We've got a few weeks yet and he's got this four-day game and he's in our Twenty20 squad for New Zealand and we've got a game against Essex leading into the Ashes, so there is some cricket left, which is encouraging."