The 23-year-old, like most players in Pompey's squad, has been on month-to-month contracts while the club were in administration.
But the future looks brighter now the Pompey Supporters' Trust has completed its takeover and former Bradford shot-stipper Eastwood wants to be part of their bid to climb back up through the leagues.
"We have some good players here and I think we could do well if we can keep the squad together," he told the club website.
"It will be challenging, but it's certainly something we are all looking forward to.
"It'll be nice to sign a proper contract. We've had a sit down and spoken about things, but I appreciate playing for a club like this."