England quick Wood frustrated by 'slow progress' in recovery from elbow surgery
Wood bowled 17 overs before suffering an issue with his right elbow in the first Test of a three-match series against West Indies, which ended in a 1-0 defeat for England in March.
The 32-year-old was forced to pull out of the ongoing Indian Premier League, where he was due to play for new franchise Lucknow Super Giants, and underwent an operation on his elbow.
Durham quick Wood hopes to use spells in Eoin Morgan's ODI team to regain fitness, with the three-match Test series against New Zealand that starts on June 2 at Lord's proving a step too soon.
England then face India in the rescheduled fifth Test in July, and Wood may target the visit of South Africa for three Tests in August and September as a potential return.
"Every time I bowl there's still a bit of swelling," said Wood, who was speaking at an event for England Test sponsors LV= Insurance.
"I'm hoping I can get off my full run in the next couple of weeks then play for Durham after that.
"At the minute it's a little bit slow going. The back-end of the summer is where I'll be looking at for Test matches, nothing early doors.
"If I can build up through one-day cricket first, that would make it easier for me to come back into Test matches."
Wood is one of seven pace bowlers sidelined for England's first Test against New Zealand, with Olly Stone, Sam Curran, Chris Woakes, Jofra Archer, Saqib Mahmood and Matt Fisher all out of action due to injury.
Ollie Robinson was also not considered for Brendon McCullum's new England Test squad due to fitness issues, which opened the door for a maiden call-up for Durham's Matty Potts.
Potts is the leading wicket-taker in the County Championship this season with 35, claiming 7-40 in a win over Glamorgan last time out, and Wood knows firsthand the qualities of his Durham team-mate.
"He's a proper bowler," said Wood. "He's got something about him and finds ways to get wickets. He's a big, strong lad, built like a tank.
"He never seems to drop off. He's really fit, constantly running in and making things happen. When you think nothing is happening, he gets a wicket. That's a great knack to have."