Gerrard is today being linked with Real Madrid.
"Gerrard is an exceptional player and he will be thinking 'where's the new player to help me win things here?'," said Keegan, "because he hasn't won much at Liverpool.
"He's 30 years of age now. There are only two decisions. You either stay at Liverpool, and try and win the title there - or you make a late move to somewhere else.
"He's not going to win the title [there]. Let's say Gerard can play until he's 34. You could honestly say the chances of him winning that title at Liverpool now are not great.
"Even if they started this year to do what Man City have done - and there's no indication they will - it will take one or two years. So it's unlikely."
Keegan, who scored 100 goals in 324 appearances for Liverpool, made a surprise move to SV Hamburg in 1977 when he was three years younger than Gerrard.
He said: "Will his patience be tested? I don't know him that well. I don't know how he thinks. I left Liverpool when I was 27, right at my peak.
"Now players are at their peak at 30, so he's right at his peak.
"He can achieve everything, but only if the owners show him enough encouragement. Actions speak louder than words.
"It's about how much he loves the club, how much he wants to see it progress.
"If I was him I would say to the new owners bring in a big name. Players love to see big signings coming in. At Newcastle every time I brought in a Ginola or a Les Ferdinand or an Alan Shearer, they went 'wow'.
"Liverpool haven't done that. When you sign players in their 30s, or aged 28 or 29, you're just trying to patch up. The biggest criticism I would have is: where are the young players?"