Gunners chiefs have been in talks with Sesko's agents and also Leipzig officials about a move to London for the Slovenia international.
Leipzig are seeking £50-60m to sell Sesko this summer - a range that falls within Arsenal's summer transfer budget.
And now it's emerged that Sesko has started following Arsenal on Instagram.
Meanwhile, the player's agent Elvis Basonovic insists any move away won't be rushed.
We'll never blackmail RB Leipzig
He told GiveMeSport: "Even if there may be - or will be - a strong desire of the player to move to a certain club, we will never force or blackmail RB Leipzig.
"I believe this is not the right way, because the way you actually exit from the club shows your values. Values that you are bringing into a new club.
"I can understand in very big transfers, there are a lot of different interests but no matter what, I believe in football world should be more respect. So that’s why we do things in the right way or we don't do them.
"It’s very simple, even maybe in the media it looks very complicated.
"(Sesko's) numbers at his age compared to some strikers with already great careers at his age are confirming my words.
"He will move from RB Leipzig only when we recognise a special club, a special project with a special coach."