The UK, the Netherlands and the Czech Republic at a meeting of EU diplomats in Brussels on Wednesday (22 July) spoke out in favour of opening EU missions to third parties in principle.
The UK is at the same time exploring potential French and German backing for a Georgian request to invite US monitors to join the EUMM.
Some member states fear that a US presence would make the EU mission a target for attacks by Georgian separatist forces, however. EU officials also worry that the move could damage ongoing peace talks between Russia and Georgia in Geneva.
The discussion comes after Russia earlier this year pulled the plug on UN and OSCE observers in Georgia.
The withdrawals will leave the EUMM´s 313 unarmed officers and administrative staff as the only international entity in the post-conflict theatre.
"There should be an interest from all sides in building bridges with the US or other parties to make sure there is a wider presence, both institutionally and on the ground," Georgia´s EU ambassador, Salome Samadashvili, told EUobserver.
US vice president Joe Biden on a visit to Tbilisi on Wednesday ducked press questions on prospects for US deployment. But a US official told this website that the US is "consulting with the EU and Georgia on the best way forward."
"We believe a robust international monitoring presence is critical to conflict resolution," the contact said.
Georgia has indicated that Turkey would also be a welcome addition to the EU team, with Turkey on Wednesday sounding a positive note.
"That would fit in quite nicely with our general support for any and all efforts to improve stability and well-being in Georgia," Turkey´s foreign ministry spokesman Burak Ozugergin said.
EU foreign ministers meeting on Monday are expected to extend the EUMM´s mandate for a further 12 months until 14 September 2010.
The EUMM can be enlarged to include other countries at any time following a unanimous decision by EU states. But a formal discussion on enlargement is not foreseen before September, when EU institutions resume full activities after the summer recess.