Arsenal transfer news: Neil Lennon would not be surprised if Gunners submit improved offer for Kieran Tierney

Arsenal are believed to have had two bids rejected for the Scottish left-back

Celtic manager Neil Lennon would not be surprised if Arsenal submit an improved offer for Kieran Tierney.

The Scottish champions have already rejected two bids from Arsenal for the left-back, who is not yet back in training after a double hernia operation and pelvic issues.

“Normally these things tend to happen again so it wouldn’t surprise me, put it that way,” Lennon said. “That’s not from personal knowledge of anything, that’s just my own experience of things.

“We know the (Premier League transfer) window shuts on Thursday so if we are talking about Arsenal then they have five or six days to come back in with a revised offer.

“Apart from that we will continue on and get Kieran back with us and fit as quickly as possible because he is such an important player.”

Kieran Tierney remains a transfer target for Arsenal (Getty)

Despite confirming the signing of Nicolas Pepe this week for a club record fee, Arsenal are believed to still be keen on bringing Tierney to the club, with Unai Emery looking to add to his options at left-back.

A figure of £25 million is believed to have been quoted, but Arsenal have so far failed to match Celtic’s valuation up front.

Lennon is also preparing for interest in other squad members ahead of the window’s close.

“I imagine there will be offers coming in,” he said. “For certain individual players the asking price hasn’t been met and the clubs know what the asking price is. Until that valuation is met we thankfully don’t have a decision.

“But the closer it comes to the end of the window, and then something crops up, we are prepared for that aspect of it, but it’s not welcome.”

Lennon confirmed there would be no new additions at Celtic Park ahead of their third Champions League qualifier against Romanian club Cluj.

When asked if he was close to signing anyone ahead of Saturday’s Ladbrokes Premiership opener against St Johnstone, Lennon said: “No, we will have a quiet weekend.

“At the minute we are content with what we’ve got and we will go into Saturday and Cluj with the squad we have.”