Sterling, who turned 18 earlier this month, is set to sign a five-year contract in the coming days, warding off interest from the likes of Manchester City and Chelsea. Sterling's progress has been swift since arriving from QPR aged 15 but Marsh, who was coaching at the academy at the time, instantly knew they had a star in the making.
"I was his coach on the night he came for his first day of training in the under-16s," said Marsh, who was promoted from under-18s manager to Brendan Rodgers' coaching staff. "He was only 15 and the local lads - they're quite feisty - decided to test him in one or two challenges and he didn't shirk a challenge."
Marsh added: "He was just straight back into the next one and I thought 'We've got a player on our hands'.
"Talent isn't everything but when we're talking about bottle we're expecting him to be brave and get on the ball in areas when he can hurt defenders. You can see he's got a bright future."
Press Association Sport understands Sterling, who made his senior England debut last month, could sign the contract by this weekend.
It is just reward for the rapid progress he has made since arriving from QPR in February 2010 on a deal which still has 18 months to run.
After making his first-team debut in March under former manager Kenny Dalglish, Sterling has become a regular starter under Rodgers and the club were keen to tie him down to a longer contract as soon as he turned 18.
There were some sticking points over wages, which alerted a host of top clubs, but an agreement has been reached which satisfies all parties.
Liverpool were keen not to be held to ransom on the salary issue, wary of paying the youngster too much too soon, but it is believed Sterling's new contract will be incentivised and include a number of performance-related increments.