Sam Allardyce’s team are currently 10th in the Premier League table with 39 points from 28 matches, 12 points behind fifth-placed Liverpool.
The Hammers have lost their last two league matches and have been struggling for form for weeks, which has had an adverse effect on their European chances.
However, Jenkinson, who joined West Ham on a season-long loan deal from Arsenal in the summer of 2014, is refusing to give up hope.
“It’s time to regroup and we've still got a very important run-in until the end of the season,” the 23-year-old West Ham’s official website following Wednesday’s 1-0 home defeat to Chelsea.
“We want to be as high up that table as we possibly can. A European place is what we’ve targeted up all season and that’s still the case. I think that’s realistic.”
Can West Ham qualify for Europe?
Given the league table and the current form of West Ham, it is very unlikely that the London club will finish in a European place.
West Ham are no fewer than 12 points behind Liverpool, who are on a great run of form and could well finish in the top four.
Tottenham Hotspur and Southampton are very close to Liverpool and are fighting for a top-four finish as well.
The best Allardyce’s side can hope for this season is a top-10 finish in the Premier League.