Arsenal have already had two bids turned down by Celtic for Tierney.
But Solhekol claims an offer of £25million, with more money up front, would be enough to prise the Scotland international away from his boyhood club.
If he joins, Tierney would add to the signings of Dani Ceballos, William Saliba and Gabriel Martinelli at Arsenal this summer.
The Gunners are also said to be close to completing a deal for Lille winger Nicolas Pepe after reports claimed they have agreed a £72m fee with the Ligue 1 side.
So Tierney and Pepe would take Arsenal’s incomings to five in this window.
“Well this is a story that we’ve been looking at all day today, trying to get a development for our viewers,” Solhekol said of Tierney.
“One source close to the deal was able to update us this afternoon.
“What they said is, I’ll read out the message they sent to me, Arsenal increasingly confident that a deal with Celtic with Tierney is edging closer.
“Still no third official bid yet but talks suggest all parties will be happy with the numbers when that is finally registered.
“Now that is a message that we got this afternoon, seeming to suggest that Arsenal are edging closer to signing Tierney.
“Good news you’d think for Arsenal supporters.
“We took that information and we put it to a source very, very close to Kieran Tierney to see if they would back that up.
“Unfortunately they came back to us with a very, very short message which was ‘not true at this time’.
“So we’re getting mixed messages about what is happening with Kieran Tierney.
“But through all the fog, I think we can say if Arsenal come up with £25m and structure that deal so it is more front-loaded, Celtic are willing to let him go.”