Standard Life, which holds 7.5% of the shares said that it hoped GCap would "engage" with Global, and Schroders, which owns more than 16%, is said to hold the same opinion.
David Cumming, head of UK equities at Standard Life Investments, said: "Due to the increased offer, it is appropriate GCap engage with Global Radio with a view to accepting the revised bid."
Global, owner of the Heart and Galaxy radio brands, made what it called a third and "final" offer for GCap yesterday at 225p a share in cash, conditional on the recommendation of the board.
The bid values the UK's biggest radio firm at £370m, around 20% higher than Global's original offer of £313m in December.
Global's second offer of 202p a share was swiftly rejected last week by GCap, which stated that it "significantly undervalues" the company.
The Takeover Panel has imposed a deadline on Global Radio to bid or walk away by 5pm today, but one of the conditions of Global's offer is that GCap acts to extend the deadline to April 2.
Last month, Fru Hazlitt, chief executive of GCap, outlined a cost-cutting and refocusing plan that she said would target operating margin ranges of 12%-14% in the year ending March 2009 and 17%-19% in the year ending March 2010.