Royals manager Alan Pardew has been tracking the centre back as he searches to find cover for injured defenders Adie Williams, Matt Robinson, John Polston and Chris Casper.
Pennock still has a year-and-a-half left to run on his Gills contract and Hessenthaler (pictured) has made it clear that he wants to keep the stopper at The Priestfield Stadium.
"I heard local radio reports saying that we will not renew Adrian's contract," Hessenthaler told the Reading Evening Post.
"I don't know where they got that from - he's got over a year-and-a-half left and I want to keep him.
"If Reading are interested in him, I can tell them now he's not for sale as he's playing out of his skin and, as far as I'm concerned, I want him playing for this football club."
Pennock's is the latest in a long list of names to be linked with The Royals along with fellow Gill Nicky Southall, Bolton's Anthony Barness, Portsmouth's Adrian Whitbread and Dundee United's Neil Heaney.
Pardew has stated that he is looking for a wide midfield player and it would seem that Heaney fits that description.
It is reported that Reading have made enquiries regarding the player`s availability, although no official approach has been made to the Scottish Premier League strugglers.
