Government agencies had "advised" Saeed not to participate in public rallies for the time being, unnamed associates of Saeed were quoted as saying by The Express Tribune newspaper.
PML-N leader Pervez Rasheed, the spokesman for the government of Punjab province, said he was not aware of any such request made by authorities.
Saeed's aides claimed the suggestion was made because the government fears the Jamaat-ud-Dawah chief's continued appearances might draw a "hostile reaction" from the US.
They said Saeed was "adamant" and would not accept any such demand.
The aides said Saeed planned to address a rally organised by the Defa-e-Pakistan Council in Quetta, the capital of Balochistan province, later this week to mobilise people against any move by the government to reopen supply routes to Afghanistan that were closed after a cross-border NATO air strike killed 24 Pakistani soldiers in 2011.
Unlike other terrorists sought by the US, Saeed lives openly in Lahore and has mocked the bounty offered for him, saying he is ready to face "any American court" to answer charges. The US also offered a two million dollar bounty for Saeed's deputy Abdul Rahman Makki.
The Defa-e-Pakistan Council, a conglomerate of over 40 extremist and hardline groups cobbled together by Saeed, has organised protests against the US bounty across the country in recent days.
The Pakistan government has sought "concrete evidence" against Saeed and Makki from the US, saying this was necessary to "proceed legally" in the matter.
Following the Mumbai attacks, India provided Pakistan several dossiers with evidence against Saeed and other members of the LeT and JuD who were linked to the terrorist assault.
Pakistan has maintained that this evidence is inadequate to prosecute Saeed. Saeed was detained for less than six months after the Mumbai incident before being freed on the orders of the Lahore High Court.