The 31-year-old midfielder has been recalled for the World Cup qualifiers against Germany and Kazakhstan later this month by interim boss Noel King.
The call-up is the first time that Reid has been included in the Ireland squad since a disagreement with former manager Giovanni Trapattoni five years ago.
"I am very pleased. Any player we get called up for international duty makes us very proud," Davies told the Nottingham Post.
"The club are proud to get representation in any international team. So we are pleased. The players have to go and enjoy it, to enjoy being part of the squad and playing for their country. That is a very proud moment for them and their families.
"We will keep our fingers crossed that we get them back fresh and fit. That is important."
Reid has scored four goals in 27 appearances for Ireland.