Kemp said he had been approached by long-serving Bournemouth Poppies defender Jackson and Warren, who finished as the Victoria Park club’s joint-top scorer in the league with 13 goals despite ending the campaign with Blackfield & Langley.
However, with 17 of his existing squad already committed to the cause, the County Ground manager insisted any new faces would have to stand out during pre-season to make the cut.
Kemp told the Daily Echo: “I had a chat with those two and told them they would be welcome at pre-season training. They came to me but with most of the squad secured early on we wouldn’t be in a position to offer them much in the way of money.
“It is a good thing because I am a great believer that players need to make the effort to join clubs at this level. I have learned from past experience that you can spend weeks trying to sign a player only to lose them as soon as things go a little bit wrong.
“We will leave the ball in their court and see what comes of it.”
All of the players who helped Hammers finish last season with a flourish have signed on apart from former Wimborne Town midfielder Micky Hubbard.
Kemp added: “After last season, Micky wants to take his time and make the right choice which is understandable.
"He was a bit flat having been at Wimborne and Blackfield and made it clear he didn’t want to become a journeyman.
“I would love him to stay with us but equally, he needs to be somewhere he wants to play.”