Westwood, capped 21 times by his country, missed out on an international call-up last week ahead of Ireland's forthcoming European Championship qualifiers with Georgia and Switzerland.
Ireland boss Mick McCarthy has held talks with Westwood and told him he is unlikely to start ahead Middlesbrough’s Darren Randolph.
"From a selfish point of view, I am delighted," said Monk. "I want as many players with me as possible.
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"But I have worked with a lot of international players and you are also proud as a club when they represent their countries. It is important to have that.
"It is always down to them and their international managers whether they are selected or not.
"But, obviously, when you have got players here and they have not gone away it is a much bigger benefit for me and for the team to be able to work with them."
Westwood, 34, produced two important saves as the Owls dug deep to beat Wigan Athletic last weekend, including a stunning reflex stop to keep out Kieffer Moore's header in the second half.
Monk said: "We know what quality he has. He didn't have a lot to do but was there in the one or two moments that we needed him."
The Republic of Ireland's loss is Sheffield Wednesday's gain.