Speaking at his news conference ahead of Saturday's clash with Burnley, Bilic said: "He needs to be consistent, play well, score goals and make an impact on a regular basis for West Ham, to think about an England call-up".
But given Carroll's aerial prowess, some pundits have called for his inclusion in Gareth Southgate's squad for Russian Federation.
Asked if he can be a force at global level, Carroll added: "Definitely".
"It would be nice to be in the squad", he told Sky Sports.
"I am feeling good".
"If I deserve it, hopefully I will get the call".
"I just hope to return to West Ham as a more experienced player, ready to play in the Premier League or any league".
"I am feeling a lot sharper than I did at the beginning of the season, getting back fit".
"In training, I feel a lot sharper, not 100 per cent yet but I am getting there".
Sakho has tough competition ahead of him in the striker position with Javier Hernandez and Andy Carroll ahead of him in the pecking order, but the Hammers have been impressed with his professionalism and are looking to give him more opportunities.
With West Ham now hoping to secure a deal, the Hammers may bring in Simpson in January, and either loan him out or leave him in their development squad for the foreseeable future.
West Ham manager Slaven Bilic has revealed that he has been working his socks off with two attacking players in his squad to improve the team's results in the upcoming weeks.
"It's a motivation and it's the same for Andy Carroll". West Ham needs to string a run together.