The 19-year-old netted an impressive 23 league goals on loan at Bristol City in his first full season as a senior footballer.
Jenkins said: "I know Paul has spoken to John and his agent".
But sources close to the player say he is still not convinced a move to Newcastle is the best one for him at this stage of his career.
"It is a slow market as the players have been away on worldwide duty".
"Our aim is to try and keep Gylfi and Fernando, keep our better players and to make sure we can add to (the) squad".
"Llorente had such a good season, it has worked well for him and the club after his season with Sevilla, where he did not play as much as he would have liked". "Paul has a fair bit of money to consider and there are one or two players we are looking to get signed".More news: Hire firm 'shocked' to see their van used in mosque attack
But despite the evident attention from Ronald Koeman's men, who are able to offer Europa League football, the Icelandic worldwide is not itching to leave The Liberty Stadium and was recently slapped with a £40m price tag, according to The Liverpool Echo.
"Gomis (moving) to Galatasaray is possible, we have been talking", Jenkins confirmed.
"With Gylfi we know how he helps our team with his assists and goals, he is a dead-ball specialist and has caused a lot of problems for opponents and won a lot of headlines".
"Those are our main focuses, but there may be one or two other areas if some fringe players leave the club, as some a year ago didn't get enough game time". The main positions we are looking for [with the way that we play] is a central midfielder and a second striker.
'Those are our main focuses, but there may be one or two other areas if some fringe players leave the club, as some a year ago didn't get enough game time'.