The former Plymouth Argyle and Ross County manager joined the Bantams earlier this month after guiding Morecambe to victory in the League Two play-off final at Wembley.
It has been a busy start for Adams, with Andy Cook and Abo Eisa signing deals during his first couple of weeks at Valley Parade.
Cook had spent the second half of last season on loan from Mansfield Town but will return on a permanent basis next season after penning a two-year deal.
Other contracts have been agreed with more transfer targets, with the Bantams waiting for successful medicals to go through before finalising the deals.
"We have got players we have agreed contracts with, we just need to get them through their medicals," Adams told BBC Radio Leeds.
"We will be in a much better position compared to a few weeks ago."
He added: "We have made a number of signings that nobody knows about at this moment in time and that will come to fruition in the next couple of weeks."
Adams is keen to bolster his forward options but admits that it is not a straightforward task.
He continued: "We will look to add to that area in the coming weeks. We have to sign the right type of centre forward.
"The market is difficult. We are doing our best to try and get in another striker."
He continued: "We have still got work to do. We have about four new signings to make and we haven't entered the loan market yet.
"I would say we are in a very good position at this stage in the transfer window. To only have four players to get with the remaining time, it has been a very good two weeks."
Bradford players are set to report for pre-season training on June 28.
In an ideal world, Adams would like to have his entire squad together on that date but admits: "I always want to have the full squad but it is never that easy to do. If I can get the majority of the squad in then I will be delighted with that."
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