Joe Cole had waited 20 months for a Premier League goal and could not celebrate when it arrived. It reflected well on Cole's character to respect the club that shaped him but illustrated his fortunes at Liverpool that a rare moment of release had to be restrained at West Ham.

Cole has been frustrated at every turn since joining Liverpool on a free transfer from Chelsea in July 2010. There have been too many false dawns on Merseyside to believe Cole's career will finally take flight at Anfield following an impressive showing at Upton Park, or that Brendan Rodgers would resist an offer to remove the 31-year-old from a wage bill he is under instruction to reduce should one arrive next month.

The Liverpool manager, Cole's third in his time at Anfield, has never started the former England international in a Premier League game. The forward played well and scored in his last start for the club, against Young Boys in the Europa League, when the headlines all belonged to him until the Swiss side equalised in the 88th minute, but was back to the bench at Swansea on the Sunday. "It's been a tough few weeks after the Young Boys game where I thought I had [earned] a start," he admitted. "I haven't trained for two weeks but to come back [at West Ham] and do well, hopefully that will kickstart the season."

In fairness Cole has never ducked a question about needing to launch his Liverpool career, however repetitive they have become. The pattern was established on his Premier League debut for the club, against Arsenal, one that ended with the first red card of his professional career, and has not changed more than two years on as injuries have impacted on his opportunities, pace and form.

Rafael Benítez thought that was the case in early 2010, the legacy of the cruciate ligament injury Cole had suffered at Southend in an FA Cup tie 12 months previously, when Liverpool's former managing director Christian Purslow first broached the possibility of the transfer. The fact Purslow pressed on with a deal that would see Liverpool pay Cole more than £100,000 a week for four years told Benítez all he needed to know about his own Anfield future.

Liverpool's generosity is no fault of Cole's but, having returned refreshed from a successful loan spell last season at Lille, who want him back in January, a series of hamstring injuries denied him the chance to make a positive first impression on Rodgers. He lasted 23 minutes of the new manager's debut at FC Gomel in the Europa League qualifying rounds, was out for two weeks, returned as a substitute in Rodgers' first Premier League game at West Bromwich Albion and suffered a recurrence nine minutes later.

West Ham, however, Young Boys and the spell at Lille demonstrated that Cole has reason to believe in a fresh start, wherever that may be. He said: "When I came off the pitch after scoring against Young Boys, considering I haven't done much for Liverpool, the reception I got from the fans was amazing and it meant a lot to me. The fans can see I want to do well for this club and it was great to score a goal for them and get the three points. I really do think this team is making good progression. The players are getting better and better and really responding to the things the manager wants us to do."

As a former young English talent who carried huge expectation, Cole is well placed to advise Raheem Sterling as Liverpool attempt to secure the 18-year-old on the first senior contract of his career. He said: "He is a real livewire and is always a threat. He never stops running and working hard for the team and never looks tired, and for an 18-year-old kid that's unbelievable. He is going to be a top player and he is at the right club to do that."