However, Keen has no formal managerial experience, apart from coaching West Ham's reserve team.
Allardyce conceded several of the Hammers' big names, including Scott Parker, Carlton Cole and Robert Green, are likely to leave the club in the summer.
But he revealed he has been told by the club's owners how much money he will have to sign new players, in a bid to get the club promoted next season, although he refused to disclose the figure.
"At the moment only Matthew Upson has left," he told BBC Radio 5 live. "It's likely [other] players may leave but the financial support from the chairman and the board will help me to cover those players.
"I'm very impressed with the facilities and the determination of the chairman and the board to get back at the first attempt, which will give me the support to try and achieve everybody's goals."
Allardyce's reputation for using long-ball tactics has led some to question how he will fit in at West Ham, a club with a tradition of playing neat, attractive football.
But Allardyce insisted that would not be a problem: "That history that West Ham have I am very well aware of and we will play the West Ham way with the players we have got to achieve the ultimate, and that's winning football matches.
"It's a challenge for me to use my experience to get them back in the Premier League as quickly as possible. It's a very exciting prospect for me and one I'm looking very much forward to."
The Lancashire club slipped deeper into the battle to avoid the drop following Allardyce's exit, and were only guaranteed another season in the top flight by beating Wolves 3-2 at Molineux on the final day of the campaign.
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