O'Neill is currently plotting how he can make his mark on the squad he inherited following Giovanni Trapattoni's sacking in September - a slightly frustrating task given a three-month wait before his next fixture.
O'Neill, along with assistant Roy Keane, was in the dugout for the first time during November's friendly double header against Lativa and Poland, but took charge of a squad initially selected by caretaker coach Noel King.
He will put his own group together for the March 5 visit of Serbia and the 61-year-old would be interested in hearing from Given, who retired on 125 caps last summer and is currently 37.
After being relegated to the Aston Villa bench, Given has been revitalised by a loan move to Middlesbrough and could provide serious competition for the likes of Keiren Westwoood and David Forde.
"I would not discount that at all," said O'Neill.
"I haven't spoken to Shay but I would like to at some stage, if he says 'I'm back'.
"But I am having a conversation here about somebody I haven't actually spoken to. I know Shay and I've spoken to him a number of times but that was before I took the job on.
"I may be a million miles out of my ground because he may have no intention of coming back, but I certainly wouldn't discount it if I'd had that conversation and he was thinking about coming back."
O'Neill is keen to add to his options in any way possible and has previously suggested that West Ham's former England Under-21 international Mark Noble could be offered the chance to switch allegiance, while he would happily end Stephen Ireland's self-imposed exile.
The assessment of age-group players - as well as the identification of players such as Norwich winger Nathan Redmond who, like Noble, may be eligible to play for the Republic through familty ties - also promises to occupy O'Neill's time.
"Some players the previous manager maybe felt weren't his cup of tea, I might disagree on and vice versa, that's always the case as a manager," he said.
"But I've certainly seen on or two players who have interested me.
"One or two are doing well at the moment and I would like to bring them into the squad and there are one or two other younger lads that I've been quietly impressed with.
"I don't want to individualise now but young Nathan Redmond (a current England U21) plays at Norwich and I'm aware there might be some kind of connecction."
Regardless of the tasks O'Neill has set himself, the next few months will be different from any other in his coaching career.
He has rarely been out of the day-to-day club game in 25 years since starting out as a boss but must now maintain a watching brief as his new charges get on with their domestic duties.
"When we came back from the last game in Poland (in November) it was interesting...we said 'cheerio' to the players and then I don't see them collectively again until March," O'Neill added.
"Of course I will watch them play but I did think that was really strange and it didn't hit home for a day or two. But as the weeks go on you get to see more games and it gets easier.
"The point about club management as opposed to international management, I knew it existed but it was kind of strange.
"I'll get to see as many games as possible, with Roy covering other matches, and we'll collate information.
"It's now about gathering as much information as I can and seeing as many players I can."