Celtic are preparing to lodge another offer for Torino midfielder Gvidas Gineitis, according to transfer reports, with the Serie A club reportedly holding out for a fee in the region of £12m for the 22-year-old Lithuanian international.
Across Glasgow, Rangers are said to be advancing in talks with newly-promoted Premier League side Coventry City over a potential deal for winger Jahnoah Markelo, 23, as the Ibrox club continues to strengthen its attacking options ahead of the new season.
Elsewhere in Scottish football's transfer market, Dundee United full-back Will Ferry is reportedly attracting interest from Belgian outfit Anderlecht, who are believed to be in discussions to sign the 25-year-old. Ferry has also caught the eye of newly-promoted Bundesliga club Schalke 04, who were reported to have had scouts watching him during Dundee United's draw with Rangers at Tannadice on Friday.
Celtic, meanwhile, look set to part ways with right-back Alistair Johnston this summer, with a fee of around £14m expected for the Canada international. Everton and Fulham are said to be the two clubs most keen on securing his signature.
At Ibrox, Scotland defender Scott McKenna is not currently viewed as an active target for Rangers. The club had explored the possibility of a loan move for the centre-back from Dinamo Zagreb several weeks ago but has since shifted focus toward signing Olwethu Makhanya instead.
On the injury front, Celtic manager Martin O'Neill has moved to dampen speculation over incoming central defensive reinforcements. With Cameron Carter-Vickers having returned to full training following an Achilles injury, O'Neill indicated there are no immediate plans to bring in a new centre-half, suggesting the club is satisfied with its current options at the back for now.
In other transfer news linked to both halves of the Old Firm, Algeria winger Fares Ghedjemis remains a player of interest for Celtic and Rangers alike. However, doubts have emerged over his immediate future at Frosinone after he was left out of the squad for the club's pre-season friendly against Benevento, fuelling speculation that a move away from the Italian club could be on the cards.
Finally, former Rangers captain James Tavernier continues to draw interest from abroad following his departure from Ibrox as a free agent in May. French clubs Paris FC and Nice have both been credited with interest in the experienced right-back, who spent close to a decade at Rangers and was a key figure in some of the club's most successful recent campaigns.
With the transfer window well underway, both Celtic and Rangers appear to be busy on multiple fronts, balancing incoming and outgoing business as they look to shape their squads for the upcoming season. Neither club has confirmed official positions on most of the reported deals, and further developments are expected in the coming weeks as talks progress on several fronts.
Based on reporting from BBC Sport Football.