"You can expect some news either later today or tomorrow," the Englishman, who turns 33 on Friday, told local daily newspaper Today on Wednesday.
Former England under-21 winger Pennant has been looking for a new club since leaving Wigan Athletic in June following their relegation to the third tier of English football.
The newspaper said Pennant would be taking a 70 percent pay cut to join "the Stags".
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"The monetary hurdle has been crossed long ago. I knew before I flew here I would have to take a big pay cut but you must look at the bigger picture," Pennant said.
"If you do well for the S.League and Singapore football, you will be rewarded in different ways and, in the long run, it may be a no percent pay cut.
"Furthermore, there are other things here in Singapore that I value much more than money," he added, citing the wealthy Southeast Asian city-state's low crime rate, cleanliness and lack of language barrier.
The transfer, when completed, is the latest surprise twist in a career that promised so much when Pennant left Notts County and signed for Arsenal aged 15.
Undeniably talented, his career was hit by indiscipline, arrests and jail time for drink driving offences and he became the first footballer to play a Premier League match whilst wearing a police tag in 2005.
Spells in Spain and India followed, before Pennant flew to Singapore last week to undergo a week-long trial with the five-times domestic champions.
The arrival of a player with vast Premier League experienced gave a much-needed fillip to a S.League organisers struggling to gain a foothold as locals immerse themselves in the English game.
"The minute I got here, it was in the media and a few teams from South Korea, Australia and Malaysia got in touch," Pennant added.
"In fact, they offered much more than what I could possibly get here in Singapore. But the chairman has a project and I am happy with it. So, sorry to the rest but I am staying in Singapore."
(Reporting by Patrick Johnston; Editing by John O'Brien)
