Visiting the Northern Ireland Assembly earlier this week, European Parliament President Hans-Gert Pöttering said the EU would consider helping shore-up the development.
Mr Pöttering, meeting with First Ministers Peter Robinson and Martin McGuinness, pledged to raise the matter with parliament colleagues in Brussels.
"It is very useful to have a centre where you study the development of the reconciliation process," he said.
"We should learn from history, from the good developments, from the bad development.
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"We should give the lessons we take from history to future generations and I would welcome the building of such a centre," added President Pöttering.
Also referred to as Long Kesh, the jail was once one of the province’s highest security facilities, housing some of Northern Ireland most prolific prisoners.
When the Maze was eventually closed, the site was put into the hands of the Northern Ireland Assembly.
Some Unionist politicians have opposed plans for a conflict resolution centre at the site, claiming it would become a "shrine to terrorism".
Proposals for a national sports stadium on the Maze site appear to have all but collapsed.
President Pöttering visited a number of projects during his time in Northern Ireland.
The First Minister said: "Since devolution we have actively engaged with Europe in order to maximise the best possible benefit for Northern Ireland. At this time of economic instability we are determined to ensure financial and other support from all possible sources including the EU.
"This visit by President Pottering is the latest demonstration of Europe's continued interest in this region and it serves to further develop and strengthen our EU-NI relationship which will ultimately bring rich benefits across Northern Ireland," added Mr Robinson.
(PR/KMcA)
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