World Anti Doping Agency chief Dick Pound is confident Fifa will comply with tougher sanctions before the World Cup kicks off next month.
Blatter has been locked in talks over the new anti-doping code
Fifa informed Wada it will push its members to adopt the world anti-doping code at the tournament in Germany.
If adopted, players could face two-year bans for doping violations instead of lighter bans received under Fifa rules.
"Fifa president Sepp Blatter said, 'We will do this and will follow it,' so I accept his word," said Pound.
A settlement would end a year of dispute, since Wada declared Fifa noncompliant with the anti-doping code in May 2005 but decided it would give Fifa time before calling for sanctions.
"The great thing about Fifa being onside is that it's the biggest, most important sport in the world," added Pound.
"The World Cup is the only thing that rivals Olympic audiences. It's a tremendously strong message."
Wada and FIFA have been working out the details of the anti-doping code since last month, when the Court of Arbitration for Sport in Switzerland found FIFA was not in compliance with Wada's standards on eight points, including its penalties for failed drug tests.
Pound said seven of the eight points can be approved at a FIFA executive meeting and the last at a FIFA congress in Munich in the week leading up to the World Cup.
Fifa disagreed with Wada's two-year ban for offences, preferring instead that each case be judged individually with bans from six months to two years.