The Glasgow boss was delighted with the performance of his Australian-born playmaker as the Warriors secured back-to-back victories over rivals Edinburgh at the weekend.
Parks was instrumental in the 22-15 win at Murrayfield on January 2 as Glasgow cemented their position at the top of the Magners League.
"Dan's contribution was absolutely huge," said Sean Lineen.
"He enjoyed the wide open spaces that allowed us to use the ball. And he showed that he can pass as well.
"It's up to Andy Robinson what he wants for Scotland, but looking at what happened (on Saturday) you can see that Dan can control a game."
The 31-year-old hasn't featured for his country under new Scotland coach Andy Robinson but Saturday's showing suggests a recall could be a possibility for the forthcoming Six Nations.
The fact that such a commanding performance came when Parks was up against Scotland's current No10, Phil Godman, has given his case even greater merit.
While Godman was disappointing as Edinburgh dropped seven points behind the Magners League pace setters, Parks was anything but, controlling the game with his ever-consistent right boot but also standing flat and pushing Glasgow over the gain line time after time.
Parks became the first player to score 1,000 Magners League points last month and he will now be hoping for even more reason to celebrate when Robinson selects his squad for the 2010 Six Nations opener against France on February 7.
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