Ligue 1 giants Nice are also keen on Shaqiri, who won the Bundesliga and Champions League with Bayern Munich, but West Ham will look to pip them to the signature of the 26-year-old who cost £12million upon arriving England from Inter Milan in 2015.
Wagner praised Lolley after he atoned for his error by hauling his side level on the stroke of half-time with a sublime strike but the German was left frustrated after seeing Huddersfield fail to contain West Ham's creative engine of Lanzini and Arnautovic.
Hernandez and Marko Arnautovic were expected to fire the Hammers up to the top half of the table.
David Wagner admits his Huddersfield side made easy mistakes that were clinically punished during their 4-1 defeat against West Ham at the John Smith's Stadium.
The victory for David Moyes's side, which was secured with two strikes from Manuel Lanzini, has lifted them further away from the Premier League's relegation zone. The Austria global this time beat Smith to race clear into the area and again found Lanzini, who rammed home his third goal of the season.
Jonas Lossl took a goal kick and played it to Joe Lolley who had three West Ham players around him. This would be the last time the pair would be on a different wavelength as they went on to end Huddersfield's hopes of getting anything from the game.
"With the second, 11 seconds into the second half, it was a very simple knock-down and we needed to be stronger and see the danger earlier".
Arnautovic claimed his second assist of the afternoon on the counter attack, as the Austrian shrugged off the challenge of Schindler before playing in Lanzini for his second goal.
The final third of the game was played with considerably less intensity with both sides taking their foot off the gas as they awaited the full time whistle to call time on the encounter.
The former Everton and Manchester United manager explained that starting the two together, rather than choosing one and a recognised striker alongside, was a deliberate decision.
Huddersfield will have a week to prepare for their crucial trip to Stoke City next Saturday, whereas West Ham have a mid-week FA Cup replay against Shrewsbury to contend with before hosting Bournemouth on the weekend. Anybody who plays well for me, that's why I'm trying to get more than 200 wins, because you can only pick the players you think are going to get the results.