The company said it had turned down the separate approaches from Redrow and Galliford Try, but that talks with the latter continue.
Redrow suggested a share and cash deal, and Galliford Try an all-share offer.
But Kent-based Bovis rejected both of the approaches on the grounds that they did not reflect the "underlying value of the Bovis business".
It said: "The board also concluded that the Redrow proposal was not in the interests of Bovis shareholders as the cash element of the offer would require shareholders to crystallise value at the current Bovis valuation."
The company added: "Redrow subsequently indicated that it was not willing to improve the terms of its proposal and discussions were terminated. Discussions with Galliford Try are ongoing."
Galliford Try said it had offered a 7% premium on Bovis' share price at close on Friday, and that - under Takeover Panel rules - they had now got a month to submit a full takeover offer or walk away.
Shares in FTSE-250 firm Bovis were at 828p at the close of last week, valuing the firm at about £1.1bn.
Fellow FTSE-250 member Galliford Try is worth roughly £1.3bn.
Last month Bovis said it had set aside £7m to compensate customers who were sold houses that were unfinished and had electrical and plumbing faults.
The house builder said then that the experiences of a significant number of customers "fell below the high standards they rightly expected".
Bovis saw pre-tax profits for last year fall 3% to £154.7m.
The FTSE 250 firm is without a chief executive at present and is led by chairman Ian Tyler.
In January David Ritchie stepped down as chief executive after eight years in the role, weeks after a warning over profits.
House builder Bovis Homes has rejected two potential offers for the firm from rivals in the sector.