West Ham have received offers from Premier League champions City and runners up Arsenal for their captain, but are holding out for even more money.
City have had an initial bid worth £90million rejected, while Arsenal's have also seen two bids rejected.
talkSPORT understands that the Hammers want £100m, with offers so far falling short of their valuation.
Rice has been linked with Arsenal since January, and is clearly the club's top target as a midfield reinforcement, and Aluko thinks Arteta is using a crafty trick to force his employers to pay-up.
The former Chelsea, Juventus and England Lionesses striker has been working as an executive since retiring, and told talkSPORT that there could be some interesting tactics going on from Arsenal.
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"I think there's a lot of cat and mouse going on here," she said. "As a sporting director I used to do this a lot.
"I used to call up a club, a big club, and say, 'right can you put a bid in' and that would basically force my owner to put a higher bid in.
"I don't think Manchester City actually want to sign Declan Rice, I think what's going on is Arteta has picked up the phone to Pep [Guardiola] and said 'listen, Arsenal are going to do the incremental bid approach, if you put a higher bid in, that will push my owner."
Asked why Arteta would try the trick, Aluko continued: "For speed and to get the deal done.
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"West Ham obviously want a certain valuation and I don't know why Arsenal are taking this incremental approach.
"It says to me that Man City coming in later on is going to help Arsenal, because the fans are going to get on it now.
"The fans are going to say 'hold on, if you let Declan Rice go to Man City when he was our number one target, that says a lot about Arsenal'.
"I used to do it all the time and it used to work."