If completed, the sale marks a return to the city for Credit Suisse, which was last active in 2008, when it purchased Atlantic Quay.
Separately, Drum Property Group is on the verge of completing a £40m deal in Aberdeen.
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The Prime Four business park development has been pre-let to Lloyd’s Register and Drum is in talks with a North American institutional investor, according to reports in industry title Property Week.
The 100,000 sq ft Cuprum, in Cadogen Square in Glasgow’s financial district, is owned by Tristan Capital Partners.
The firm paid £23.5m for it in 2011.
The building was constructed in 2009 and is arranged over seven floors with a mezzanine above ground floor.
Axa occupies 50,000 sq ft in the property.
If completed, the deal would be a vote of confidence in Glasgow’s office market, which stalled in the wake of the Brexit vote.
Total commercial property transitions in the city fell by 59 per cent, to £280m in 2016.
The last major sale in Glasgow was Fore Parnership and Kier Property’s £23.5m purchase of 50 Bothwell Street in September, from M&G Real Estate.
The market in Aberdeen has been in turmoil since the oil price peaked in 2014.
Transaction volumes in the commercial property market dropped from more than £600m in 2014, to just £55m last year.