Sam Allardyce's side had been threatening to make a surprise challenge for the Champions League spots this season after their best ever start to a Premier League campaign.
But just three wins in 2015 have seen the Hammers drop off the pace back into mid-table obscurity and fans believe some quality additions to a squad disrupted by injuries in January could have kept them fighting for Europe.
With that in mind, the club's co-owners David Sullivan and David Gold, who last week vowed to 'once again invest significantly' in the summer transfer window, are on the lookout for players who can take the East Londoners on to a new level.
The Hammers had a £12 million bid for superstar winger Konoplyanka rejected by his club Dnipro last summer according to the Daily Mail. But West Ham could land him for nothing this time around as his contract expires at the end of the season.
They may not have to look far for someone to play on the opposite flank, either.
After wasting a then record £10.5 million on the likes of Matt Jarvis in the past, the Hammers could do a lot worse than bring in Konoplyanka's fellow Ukraine star Yarmolenko, who may be available at a knockdown price as he enters the final year of his own contract with Dynamo Kyiv.
The pair would cost in excess of £30 million in an open market but competition for their signatures will be fierce with the likes of Tottenham Hotspur and Italian giants Roma also circling.
The duo would have to be persuaded to leave Champions League group stage football behind for the bright lights of London.
But the Irons moving to the 54,000 seater Olympic Stadium in just over a year's time may help negotiations.
Still only 25, Konoplyanka is the type of world class player West Ham need to start attracting if they are to thrive in their new surroundings and seriously compete in the higher reaches of the Premier League.
He would prove popular with Hammers fans too, as he is a classy playmaker in the Eyal Berkovic mould.
While assists are his main asset, he also weighs in with goals, scoring eight in 43 games for his country and 35 in 153 matches for Dnipro.
Yarmolenko, who is also just 25, is another skilful attacker and, standing at 6ft 2, offers a more physical presence than Konoplyanka.
With 65 goals in 166 games for his club and 19 goals in 48 international appearances, signing him and his compatriot would be a serious statement of West Ham's intent this summer.