Fans marched on Wednesday night from a memorial service in the centre of the western German city to the Hannover 96 stadium where Enke played. Outside the ground there were large numbers of candles, flowers and cards.
The club said on Thursday it was considering postponing its next scheduled match at Schalke 04 on November 21.
"It's not certain yet, but we are considering it," said Hannover's manager Jörg Schmadtke. "We'll have to see how the team in doing."
The 32-year-old, who was set to travel with the Germany squad to next June's 2010 World Cup in South Africa, flung himself under a busy commuter train at a small town near Hannover on Tuesday evening after suffering from depression for several years.
His broken-hearted widow gave a press conference on Wednesday explaining how her husband had been treated for depression since 2003 and had an acute fear of failure.
After losing his place in the Germany team in September after suffering from a stomach infection, Enke sought treatment six weeks ago and his psychologist, Dr Valentin Marksel, revealed details of the goalkeeper's last desperate note.
"In the letter he apologised for his deliberate concealment of his state of mind over recent days that was necessary in order to be able to put his suicide plan into action," Marksel said.
On the day of Enke's suicide, Marksel revealed the Germany star had telephoned his local hospital to cancel a counselling appointment.
"He called off all therapy appointments for the next few weeks, until further notice, because he said he was feeling better. Unfortunately, we did not succeed in protecting him from suicide," said an emotional Marksel. "In my opinion, he was not suicidal and there was no indication that he needed to be hospitalised."
Germany's friendly against Chile on Saturday has been cancelled out of respect of Enke's death.
"I am completely shocked and absolutely empty," national coach Joachim Löw said. "In this situation nobody was prepared simply to go back to business as usual."
The entire national squad is expected to attend a public memorial service to held at 11:00 am on Sunday in Hannover 96's stadium before Enke is buried in private in his home town of Neustadt am Ruebenberge, near Hannover.
Enke leaves behind his wife Teresa and 18-month-old daughter Leila, whom the couple adopted in May after their two-year-old daughter Lara died from a heart infection in 2006.