Wigan's 2-1 victory over Newcastle was overshadowed by McManaman's high challenge on United left-back Massadio Haidara during the first half of Sunday's contest.
On-the-ball incidents cannot usually be dealt with retrospectively but if Halsey, who appeared unsighted, admits he did not see the incident, the FA has the power to investigate further.
The FA will view all available TV footage of the incident from the DW Stadium before any decision on whether to take any further action against McManaman.
France U21 international Haidara suffered potential knee ligament damage and the incident resulted in Newcastle assistant manager John Carver and Wigan coach Graham Barrow being sent to the stands as they clashed over the issue.
Newcastle manager Alan Pardew said after the match: "It is an awful challenge. The pictures speak for themselves. I thought it was a bad challenge and I was 60 yards from the incident.
"The players knew because they were on top of it and there was a lot of bad feeling about that incident when it goes unpunished. He (Halsey) said 'If I've missed it I apologise' - that was at half-time."
Wigan boss Roberto Martinez defended the character of his player but admitted that it had looked a bad challenge.
He said: "I can't really comment too much because I haven't seen the action but I can guarantee that Callum McManaman is a young man full of talent and in his debut probably showed the enthusiasm that you expect, but he's not a malicious player."