McGillvary’s first was a scrappy affair but the second was stunning solo dash from inside his own half.
He has now scored six tries in four games against Catalans this season and Anderson said of his England chances: “I’ve challenged him on that.
“His performances all year have shown he’s got ability. He just needs to start believing in himself more.
“I’m not the one who makes the decisions, but at international level you need to score tries, have pace and a physical presence and Jerry ticks all the boxes.”
On the game he added: “It was typical play-off football. There weren’t many opportunities for either side to throw the ball around.
“But we ground out the win against a very good Catalans side who had one or two of their star names back.”
Catalans coach Laurent Frayssinous said McGillvary’s first try, which came on the half-time hooter, broke his side’s resolve.
He said: “That made it 16-6 and I don’t think the score reflected how the game had gone.”
But Frayssinous vowed his side will continue fighting for a top-four place and said: “Even if there’s only a one per cent chance we’ll take it.
“In our minds we’ll approach things in the same way. We won’t take any short cuts. In training we’ll still have the same objective.”