Keane has held talks about taking up a role as Paul Lambert's number two at Aston Villa, after also being linked with the managerial position at Celtic before Ronny Deila's appointment last week.
And while O'Neill would be willing to discuss the possibility of Keane working at Villa Park while also continuing with Ireland, he is eager for the situation to be resolved sooner rather than later.
"I want to be careful about jumping the gun, because we had him signed, sealed and delivered to Celtic and that did not materialise," O'Neill is quoted as saying by the Irish Independent.
"I don't really know if [going to Villa] is something that he is going to have a serious look at.
"But if he is, then I will definitely speak to Paul Lambert and see if that kind of role can be combined.
"Nothing definitive has happened and I don't really know what sort of commitment (the Villa role) would entail.
"I don't mind it [the speculation] going on for a week or two ... [but] I don't want it to be continued right through until August time."