Jermain Defoe will find out on Sunday whether he has done enough to earn an England recall.
Defoe has scored twice in three Premier League games for Sunderland this season ahead of former Black Cats boss Sam Allardyce naming his first England squad on Sunday.
The 33-year-old put Sunderland 1-0 up from the penalty spot in the 80th minute before Jay Rodriguez equalised five minutes from time for Southampton.
Moyes said: "I wouldn't be surprised at all, because Jermain Defoe is a goalscorer.
"He has that ability to score out of very little.
"And Sam knows him, he knows him better than me because he has worked with him for longer than I have.
"From what I've seen, he is a really good pro and that's what I like about him.
"He wants to do things right, and he wants to stay in good condition.
"He is certainly not someone who is just playing out the latter days of his career.
"I'd love to have a Sunderland player in the England squad.
"We started at Everton like that, then I hoped to have two players in the England squad, then three, and build it up into a squad of top international players.
"If Jermain Defoe gives us the start we need, I will be thrilled."
Defoe was tripped by Jose Fonte for the penalty.
Moyes added: "He had one or two sniffs of chances as well, and he put one away against Man City the other week as well.
"He took his penalty kick terrifically well, and we are going to need his goals.
"I haven't seen it [the penalty] yet. But some people say yes and some people say no, so if it is a split decision the referee has to call it one way or the other.
"He's a really good finisher, and we just need to keep a check on him because he is carrying a bit of a thigh strain."
New signing Javier Manquillo, 22, made his debut for Sunderland after arriving on a season-long loan from Atletico Madrid.
Moyes added: "I thought the right-back played very well today on his debut, so there were some pluses.
"I thought Adnan [Januzaj] had some great moments for us, and there were moments where you could see what a great player he is.
"We have to raise our quality and make sure that we are winning games, not drawing or losing them."