The United States and Saudi Arabia are pushing Saleh to hand over power to his deputy under a Gulf Arab proposal aimed at ending unrest that has pushed Yemen close to a civil war.
"We believe he was seriously injured ... He is not coming (home) in the coming days, he is not coming (home) soon," the diplomat told Reuters.
The United States has been helping Yemen investigate the attack, which killed several people and also wounded the prime minister, two deputy prime ministers and the speakers of both parliamentary chambers.
The diplomat said an initial investigation showed Saleh was injured in the explosion from a TNT charge planted inside a mosque within the presidential palace in Sanaa on June 3.
A source close to the investigation, asked about the number of charges planted at the mosque, said: "It was six explosives planted inside the mosque and only one went off."
Yemeni officials earlier accused an opposition tribal coalition of shelling the palace, a charge they denied.
The Arab country has been rocked by months of protests demanding an end to Saleh's 33 year-rule, which has driven Yemen close to financial ruin.
Washington and regional ally Riyadh fear that a power vacuum and tribal warfare in Yemen will be exploited by the local wing of al Qaeda to launch attacks in the Gulf region and beyond.
The proposal by Gulf Arab neighbors calls for Saleh to hand power over to his deputy, Vice President Abd-Rabbu Mansour Hadi, who is acting president, as a step toward forming a new government and preparing for elections.
Saleh has exasperated his wealthy Gulf Arab neighbors by three times agreeing to step down, only to pull out at the last minute and cling on to power.
Jeffrey Feltman, the U.S. Assistant Secretary for Near Eastern Affairs, met Hadi and other senior Yemeni officials in Sanaa on Wednesday and is also traveling to Saudi Arabia for talks on the situation in Yemen.
"It is time for Yemeni political leaders to work together for an immediate and peaceful transition of power," Feltman told a news conference in Sanaa on Thursday.
Asked if there was pressure on Saleh not to go back to Yemen, Feltman said: "We expect the president to take a decision in the best interests of the Yemeni people. It is a Yemeni decision, not an American decision."
In an early bid to placate protesters demanding his ouster, Saleh guaranteed he would not hand power down to his son, but many Yemenis say important members of Saleh's family including Ahmed Ali remain firmly in control of the key levers of power, preventing any handover of power without Saleh's consent.
Opposition parties allied with youth activists have also insisted that Saleh formally transfer power to Hadi as a step toward a new government and democracy.
An aide to Saleh said on Wednesday his health was on the mend and that he had been receiving guests and giving instructions on day-to-day affairs in Yemen, including a power cut and fuel shortages