The Teessiders completed the signing of winger Sammy Ameobi on Tuesday and Warnock is now focusing on recruiting some badly-needed new arrivals down the middle following the close-season exits of Britt Assombalonga and Ashley Fletcher.
A number of players have been linked with the club including former Sunderland marksman Josh Maja.
Boro have been offered the chance to sign the Bordeaux striker Maja – but the Ligue 1 club will have to lower their asking price by a fair way for the Riverside Stadium outfit to contemplate doing a deal.
Rotherham United's Michael Smith - also a target of Bristol City - has also been linked with Boro, alongside Wycombe Wanderers' Uche Ikpeazu, who has a number of Championship clubs interested in his services.
Warnock, who brought in a new goalkeeping option in QPR's Joe Lumley shortly after the end of last season, said: "I have got to try and build a squad where we have a little bit more cover in different areas, especially defensive wise and then attacking-wise, we have got to score more goals.
"It has been an interesting summer and we have been talking to a number of players and I think, striker-wise, we have got another three lads who we have been talking to. Midfield (players), we (also) have been speaking to and it is just getting them over the line.
"As always, it is going to be that first couple weeks of July when it fits into place."
Meanwhile, the veteran Boro chief admits his side will have to perform a 'minor miracle' to upset the odds and achieve promotion in 2021-22, but is pinning his hopes on his side emerging from the pack next season.
Warnock, whose side finished in tenth place last term, added: "It is going to have to be a minor miracle to get promotion when you look at the teams with parachute payments coming down and the teams who missed out on the play-offs this year.
"You are talking about six teams who are really away. We are about mid-table regarding the bookies, but there is always one club who comes from out of there from mid-table range or even lower down.
"I think we need a little bit of luck - everyone does - with the main players and we saw towards the end of the season last year."