Lingard has scored eight goals in nine appearances since joining the Hammers on loan from Manchester United.
“He’s playing with full confidence. Everything he seems to do is coming off, he’s running with the ball, he’s scoring, he’s a leader in the group,” the former Tottenham midfielder said.
“For me, he has to go to the Euros because he’s fresh and in top form.”
Andy Cole agrees, telling talkSPORT: “Ultimately when you come to this stage of the season you have got to take the players in form.
“I don’t really care about, ‘oh, yeah, he, six months ago was fantastic’, I’m talking about now because the tournament is going to be when the season finishes in, what, May? Three weeks later. You have got to take the players in form and if Jesse continues this then why not?”