​Celtic full-back Kieran Tierney is set to become the subject of another bid from Arsenal this summer, with the Gunners already seeing two transfer offers turned down almost instantly.

Unai Emery's side hasn't been overly active in the transfer market so far, although they have just completed a club-record £72m deal to sign Lille OSC winger Nicolas Pépé, their fourth signing of the summer.

Despite being an obvious area for improvement this summer, Arsenal still haven't made any defensive signings - £27m star William Saliba won't be available until next season - although full-back Tierney could be set to join before the window closes next week.

Kieran Tierney

The Express claims that Arsenal are close to making an improved bit for Tierney in the next few days, with the Gunners looking to improve on their initial £15m offer for the Scotland international.

Although the club have just committed to a club-record fee, it's understood that their agreed payment structure with Lille could open up the option of making at least one other signing before the window closes.

Coupled with their recent £10m sale of Poland Under-21 international Krystian Bielik to Derby County, The Express claim that Arsenal could now finally meet Celtic's valuation as Unai Emery looks for an alternative to Sead Kolašinac.

Although Arsenal are set to be linked with a host of other names throughout the window, it's unlikely that there will be any more major significant signings after Tierney's arrival in confirmed by the club.

There has been plenty of suggestion that a new centre-back could still arrive ahead on the new season, although it's most likely to be on a year-long loan in north London rather than anything else.