The Scottish international is just one of a number of players to have been linked with a summer switch to The Hawthorns, but Pulis has insisted that they have not made an approach to the Glasgow giants.
The 59-year-old is quoted by the Birmingham Mail as saying: "We'll be heavily linked with every Tom, Dick and Harry over the next couple of weeks.
"We've not made an approach to Celtic. I've not rung Brendan up. I get on okay with Brendan. So if I was going to do anything I'd ring Brendan first."
Since signing from Dundee United at the start of 2015, Armstrong has scored 21 times in 101 appearances for Celtic.
Unless he pens a new deal with Brendan Rodgers's team, he is likely to attract plenty of interest from south of the border.