David Moyes wants West Ham to set their sights high but has no intention of making bold predictions about their chances of qualifying for Europe.
The Hammers sit seventh, just two points behind champions Liverpool, and could break into the Premier League's top four with victory at Crystal Palace on Tuesday.
A win would be West Ham's sixth in a row since the turn of the year, but Moyes insists his team are not getting ahead of themselves.
He said: "We hope that we can continue that (form), but we're not getting carried away with it and we certainly don't take it for granted. We're not going to come out at West Ham and promise something that we can't deliver.
"I wanted us to try and deliver something. I hoped that it was not going to be relegation, I hoped that we were going to be much higher than that, and we have done, we've got ourselves in a really strong position.
"We're now in a position to try and look upwards, we're trying to be ambitious in our own way. But we're also trying to be respectful for where we've come from and (to) all the teams around us as well who've got some very good teams, and some of the ones below us at this moment in time."
Despite their current league position, Moyes says he would not make it public it if he thought West Ham were capable of qualifying for Europe.
He said: "I might tell the players that behind closed doors, but I certainly won't come out and publicise it because I think quite often that's when you get shot down. But I'm trying to be ambitious, I want us to move forward.
"But I think you'd have to say that we've done quite a lot of that already this year, we've made big strides forward already and sometimes then folk want even more. I want more, but I know that it can only be small steps and we're in amongst a number of good sides.
"As I said there are also a lot of good sides below us as well and we're going to have to play really well to keep them away from us."
The Hammers have been frustrated in the transfer market so far this month and have Michail Antonio as their only senior forward heading into the remainder of the campaign.
"I would say I'm hopeful, but again I can't promise anything," Moyes said when asked about potential additions to the squad.
"We don't know, we've not got anything absolutely definite. We're trying a couple of things at the moment, but they may or may not come off, so we'll just have to wait and see."