Comedian Steve Coogan has also issued proceedings and Chris Tarrant, the television presenter, and the jockey, Kieran Fallon, are also expected to launch legal actions soon, according to a Sunday newspaper.
Actress Sienna Miller has already lodged documents in the High Court in connection with the scandal.
The latest development came after prosecutors announced they were to trawl through all the material collected by Scotland Yard linked to the phone hacking scandal in a move which could spark fresh prosecutions.
Reporter Clive Goodman and private investigator Glenn Mulcaire were jailed over the controversy in January 2007 after they admitted intercepting message.
Director of Prosecutions Keir Starmer said the "comprehensive assessment" of evidence would ascertain whether further criminal charges could be brought.
Gascoigne's solicitor, Gerald Shamash, confirmed proceedings would be issued within days.
"All being well we will probably issue this week," he said.
Mr Shamash claimed that Gascoigne was in a vulnerable mental state and that his recovery had been hindered because of the trauma of believing that his phone had been hacked.
"It has made things even more difficult for his general wellbeing," he said.
Gascoigne has been fighting drink and drug problems for a number of years and been in and out of rehabilitation clinics.
The news that prosecutors are to look at the whole phone-hacking case again has been welcomed by Labour MP Chris Bryant who believes he may have been a target of phone-hacking.
Former Deputy Prime Minister Lord Prescott, the former Labour MP for Hull East, also fears his phone may also have been tapped and reiterated calls for a judicial review into the police handling of the case.
Sienna Miller is suing the News of the World's parent company and Mulcaire, accusing them of breaching her privacy and of harassment.
It emerged earlier this month that News of the World executive Ian Edmondson has been suspended as a result of her claims. Scotland Yard detectives subsequently wrote to the Sunday newspaper asking for any new evidence staff had on the case.
Now a senior QC will re-examine material amassed as part of the original inquiry and any new evidence that has come to light.
A CPS spokeswoman said there would be a "comprehensive assessment of all material" possessed by police relating to phone hacking, following developments in the civil courts.
This will be carried out by the principal legal adviser, Alison Levitt QC.
Mr Bryant welcomed the decision. "The Met and the CPS clearly made a misjudgment when they closed the case in December."
But speaking after the announcement, Lord Prescott said: "That doesn't satisfy me.
"They have failed to uncover the evidence in the past and are now only acting on evidence that a civil case has uncovered," he added.
"I'm insisting that our application to the judge for a judicial review should continue and not be put off because the DPP has decided to do an investigation.
"I believe their role in this matter has been inadequate, as indeed has the Met Police's and I'm still pushing for the judicial review."
A News of the World spokeswoman said it would co-operate with the inquiry.