The Maine Road club may be willing to part with Taylor, after clinching the signature of Liberian international striker George Weah on a free transfer.
Pulis has made an enquiry about the 29-year-old, who faces a battle for a first-team place since the new addition this week.
City value Taylor at around £2 million but Pompey are only willing to pay around £1.5 million, which The Citizens paid Gillingham for the hitman eight months ago.
Pulis is a major fan of Taylor, who he bought before when he was manager of The Gills from Brentford for £500,000, and it is understood that Pompey could accommodate his current salary in their wage structure.
Pulis said: "I like Robert Taylor. I worked with him so I know what he is about. He can complement a runner up front very well, and drop back into midfield to make things happen.
"At the moment, they would want too much for him. But we'll wait and see."
