Verbal communication is usual for draw offers, and repeating positions is equivalent to an automatic non-verbal draw offer, which the opponent can take (= claim), or decline. So it doesn't seem very much out of line with existing custom to allow a player to explicitly state that a 'pseudo-repeat' is NOT a draw offer (so it cannot be claimed). OTOH, this is sort of implied by the fact that he does not claim the draw himself.
It seems that between non-malicious players no rule is needed at all; if one of the players can force a draw this way, and expresses his intention to do so by offering a draw, the other would sooner or later see there is no way avoiding the draw, and accept. So a rule would only have to address the problem of a malicious player, which insists on prolonging the game forever without a chance of winning. The type of player that doesn't resign in a lost position, but just abandons the game, forcing the opponent to wait out the time forfeit out of spite.
Making a rule that specifies an automatic draw will alter the game result for non-malicious players, in some cases. In general, I think that this is too high a price for dealing with malicious players; a good rule would only penalize the latter, without affecting the former. A player should always be allowed to play on if something is to be achieved, within the limits of the 50-move rule. (And even the latter is dubious on an infinite board.) To prevent abuse of that right, it seems reasonable to force a player that wants to exercise it to mention how many more pseudo-repeats he needs before he is going to break the pattern, and penalize him by a loss instead of a draw when he pseudo-repeats the position after that. This still would allow the possibility of abuse, by mentioning an impossibly large number, say a billion. But this can be solved by allowing the game to 'fast-forward' the number of mentioned repeats, and continue from there. This would in fact be a rule that would also benefit normal play.
A draw offer in a pseudo-repeat position can be seen as expressing the intent to keep repeating forever. The opponent can then decline, (like usual for draw offers), but in the case of a pseudo-repeat he must decline by mentioning a number. (Which then puts a limit on how often he can keep pseudo-repeating that position without forfeiting.) Or by doing a move silently, implying the number 0 (i.e. not being allowed any future pseudo-repeats of the position). When he mentioned a number he must then move the translating group of pseudo-repeating pieces by the mentioned number of steps before pressing the clock, and the game will continue from there with any further pseudo-repeat of the position now being a loss for him. In fact there is no verbal communication needed at all, as the declining player shows on the board how often he intends to repeat, by moving the translating sub-set of pieces.