For 25-year-old O’Connell, this has meant helping Sheffield United return to the Premier League with a morale-boosting four points from the opening two games.
England international Greenwood, meanwhile, is settling in at all-conquering French club Lyon after becoming the European champions’ stellar signing of the summer from Manchester United.
For a couple who met at school, such success has been earned the hard way with both taking roundabout routes to the top.
“It is a massive move for her,” said O’Connell about his partner’s switch from the Women’s Super League to a club that has won the domestic title in each of the last 13 seasons.
“A really tough decision. She likes her home comforts and was only round the corner from the training ground at Manchester United.
“So, it was tough to leave but the move was one she could not turn down if she wants to be successful.”
O’Connell celebrated his own promotion last April to the top flight just 11 days after Greenwood, as captain of Manchester United, had led the fledgling club into the Women’s Super League.
The Blades defender then spent a couple of weeks in France, basing himself and the family in Nice, watching his partner reach the World Cup semi-finals.
Both, it seems, drive the other on. “We met each other in school,” he added to The Yorkshire Post. “I was playing Sunday League and she was at Everton, part-time.
“Now she plays for the best club in the world and I am in the Premier League. Sometimes, you do have to pinch yourself. But in our household, you just want to get better.”
The Bramall Lane faithful could be forgiven for pinching themselves right now at the rapid rise enjoyed by their club.
United host Leicester City almost exactly three years to the day since crashing to the foot of the League One table after a last-minute defeat at Millwall.
Steve Morison’s penalty meant the Blades had collected just a solitary point from the opening four games of Chris Wilder’s reign.
O’Connell was in the side that August afternoon at The Den so can appreciate better than most just what strides the club has since made under Wilder.
“It is all a big blur,” said the Liverpudlian when asked about the intervening years.
“Things have happened so quickly you just don’t have time to think about it.”
What the defender is in no doubt about, however, is the huge role that Wilder has played in United’s rise from the foot of the third tier to eighth place in the fledgling Premier League table.
“Our gaffer is a ruthless winner,” he said. “He wants you 100 per cent full throttle in training. Train how you play. His record speaks for itself.
“His recruitment has also been about bringing in winners. That has helped the club do so well. Every player here wants to win. Every day in training, no-one slackens off or coasts. That is down to the players he has brought in.
“I love it. I am the sort who likes to train how he plays, 100 per cent on that. I am not one for pulling out of tackles or anything like that.”
In the away dugout at the Lane today will be a manager who is very familiar to Liverpool-supporting O’Connell.
Brendan Rodgers spent a little over three years in charge at Anfield and came agonisingly close to bringing the league title back to Merseyside for the first time since 1990 only to be pipped by Manchester City. Rodgers, whose side netted more than 100 goals in that 2014-15 season, was named LMA Manager of the Year.
“I am a massive Liverpool fan and watched Brendan’s team,” said the defender, such a fan of the Reds he attended last June’s Champions League final triumph in Madrid against Tottenham Hotspur.
“They were a very good team and he is a very good manager who had loads of success with Swansea and Celtic. He is trying to get Leicester to be that type of team, too. So this will be a tough game.”
O’Connell’s route to tackling Rodgers and Leicester has been a roundabout one. He started with Litherland REMYCA, an amateur club in Merseyside, before joining Blackburn Rovers’ Academy as a 17-year-old.
His professional debut came during a loan spell at Rotherham United in 2012, the first of three temporary moves away from Ewood Park as the defender tried to find his feet.
A permanent switch to Brentford followed but that non-league grounding, plus the knowledge that a player’s career can be an uncertain one, saw the defender enrol on a degree course at university that still fills plenty of his time.
“The degree I am doing is sports science,” added O’Connell, who moved to south Yorkshire from Brentford three summers ago. “I am just finishing my fourth year. Just my dissertation to do and then I am done.
“It is hard, though I can get help from the sports science boys here. Basically, my day is to come in and train. Then, go home and do two hours a night. I do that most days.
“With Alex having now gone to France, at home I just concentrate on football and my degree. I do not really have time to do anything else, such as sit there and go through Instagram. And I don’t have Twitter.
“I am someone who likes routine. I like the military lifestyle. Once you get used to it, it is easy.”