Nasdaq is yet to receive any offers and wants any indications of interest to be known by the end of business on Friday.
According to Reuters, there were institutions that were contemplating a bid but it was not clear whether they would make a move.
The chief executive of Deutsche Boerse, Reto Fracnioni, would not tell Reuters if the German stock exchange operator would be making an offer for the shares.
The Qatari Investment Authority (QIA) was rumoured to have offered about $28 a share for the stake, meaning its value would stand at about $2 billion, and the total value of the LSE over $6 billion.
Nasdaq is looking to sell its 31 per cent stake to finance an acquisition of Nordic stock exchange operator OMX.
It needs more cash to be flexible in bidding alongside Borse Dubai who have made a counter offer.
Any offer for the Nasdaq shares is believed to be subject to the approval of the LSE's chief executive, Clara Furse, according to the Independent.