Griffiths, who is chairman of the All-Party Parliamentary Beer group and Mulholland who heads up the Save the Pub Group will try to secure a debate in the main chamber on the issue.
The meeting comes as a result of the e-petition to scrap the beer duty escalator hitting over 100,000 signatures. It is the only the 12th petition to reach that milestone.
The escalator, introduced in 2008 by former chancellor Alistair Darling, puts up the tax on a pint by 2% above inflation every year, and has resulted in a 42% price since 2008.
However, attempts to get the debate were hindered by the e-petition against badger culling - which had a six hour debate in the House last week.
It is hoped that a date for the debate will be as soon as next week.