Manchester United's owners spoke to Paris St-Germain chairman Nasser Al-Khelaifi a month ago in an effort to get Sheikh Jassim bin Hamad Al Thani to increase his bid for the club.
BBC Sport has been told it was instigated by the Glazers, who have known Qatari Al-Khelaifi for years.
Sheikh Jassim and Jim Ratcliffe's Ineos Group are competing to buy the club.
The Qatari banker made a fifth offer this week with a warning he would not engage with the process beyond Friday.
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It is privately being claimed the conversation did not work as the bid for a full takeover was not increased.